Mathematics exemplar problems class 10 Solutions for Chapter 13 statistics and probability

Consider the following frequency distribution:

The upper limit of the median class is

The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is

Which of the following cannot be the probability of an event?

If a card is selected from a deck of 52 cards, then the probability of its being a red face card is

While computing mean of grouped data, we assume that the frequencies are

In the formula \overline{x}=a+\frac{f_id_i}{f_i}

For finding the mean of grouped data di’s are deviations from a of

An event is very unlikely to happen. Its probability is closest to

Someone is asked to take a number from 1 to 100. The probability that it is a prime is

Consider the data :

The difference of the upper limit of the median class and the lower limit of the modal class is

For the following distribution:

The modal class is

When a die is thrown, the probability of getting an odd number less than 3 is

If an event cannot occur, then its probability is

If the probability of an event is p, then the probability of its complementary event will be

If P(A) denotes the probability of an event A, then

The probability that a non leap year selected at random will contains 53 sundays is

A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is

A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought?

One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is

A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from house D and rest from house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from A, B and C is

State whether the following statment is true or false.

If you toss a coin 6 times and it comes down head on each occasion. Can you say that the probability of getting a head is 1?

In calculating the mean of grouped data, grouped in classes of equal width, we may use the formula \overline{x}=a+\frac{f_id_i}{f_i} where a is the assumed mean. a must be one of the mid-points of the classes. Is the last statement correct?

The median of an ungrouped data and the median calculated when the same data is grouped are always the same. Do you think that this is a correct statement?

State whether the following statment is true or false.

When we toss a coin, there are two possible outcomes—head or tail. Therefore, the probability of each outcome is 1/2.

A game consists of spinning an arrow which comes to rest pointing at one of the regions (1, 2 or 3). Are the outcomes 1, 2 and 3 equally likely to occur?

The median class and modal class of grouped data always be different?

Apoorv throws two dice once and computes the product of the numbers appearing on the dice. Peehu throws one die and squares the number that appears on it. Who has the better chance of getting the number 36?

A student says that if you throw a die, it will show up 1 or not 1. Therefore, the probability of getting 1 and the probability of getting not 1 each is equal to 1/2. Is this correct?

State whether the following statment is true or false.

I toss three coins together. The possible outcomes are no heads, 1 head, 2 heads and 3 heads. So, I say that probability of no heads is 1/4.

State whether the following statment is true or false.

If I toss a coin 3 times and get head each time, should I except a tail to have a higher chance in the 4th toss?

In a family having three children, there may be no girl, one girl, two girls or three girls. So, the probability of each is ¼. Is this correct?

State whether the following statment is true or false.

Sushma tosses a coin 3 times and gets tail each time. Do you think that the outcome of next toss will be tail?

State whether the following statment is true or false.

A bag contains slips numbered from 1 to 100. If Fatima chooses a slip at random from the bag, it will either be an odd number or an even number. Since this situation has only two possible outcomes, so, the probability of each is 1/2.

The weight of coffee in 70 packets are shown in the following table:

If the modal weight is 201.7 kg then find the missing frequency.

The weight of coffee in 70 packets are shown in the following table:

What is the modal class of given data?

The mileage (km per litre) of 50 cars of the same model was tested by a manufacturer and details are tabulated as given below :

Find the mean mileage.

The daily income of a sample of 50 employees are tabulated as follows:

Find the mean daily income of employees by the assumed mean method.

The weight of coffee in 70 packets are shown in the following table :

Determine the modal weight.

Two dice are thrown at the same time. Find the probability of getting different numbers on both dice.

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is 1?

Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3 respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting each sum of 4.

Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3 respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting a sum of 6.

A letter of English alphabets is chosen at random. Determine the probability that the letter is a consonant.

Find the mean of the distribution :

The following table gives the number of pages written by Sarika for completing her own book for 30 days :

Find the mean number of pages written per day.

Calculate the mean of the scores of 20 students in a mathematics test :

Weekly income of 600 families is tabulated below :

Compute the median income.

Two dice are thrown at the same time. Find the probability of getting same number on both dice.

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is 7?

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is a prime number?

Two dice are thrown at the same time and the product of the numbers appearing on them is noted. Find the probability that the product is less than 9.

Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3 respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting a sum of 9.

Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3 respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting a sum of 7.

All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1, similar value for other cards, find the probability that the card has a value 7.

A bag contains 10 red, 5 blue and 7 green balls. A ball is drawn at random, Find the probability of this ball being a green ball .

A bag contains 10 red, 5 blue and 7 green balls. A ball is drawn at random, Find the probability of this ball not being a blue ball.

A bag contains 10 red, 5 blue and 7 green balls. A ball is drawn at random, Find the probability of this ball being a red ball.

The King, Queen, and Jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is 10 of heart.

The King, Queen, and Jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is a club.

All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1, similar value for other cards, find the probability that the card has a value greater than 7.

All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1, similar value for other cards, find the probability that the card has a value less than 7.

An integer is chosen between 0 and 100. What is the probability that it is divisible by 7?

There are 1000 sealed envelopes in a box, 10 of them contain a cash prize of ₹100 each, 100 of them contain a cash prize of ₹50 each and 200 of them contain a cash prize of ₹10 each and rest do not contain any cash prize. If they are well shuffled and an envelope is picked up out, what is the probability that it contains no cash prize?

An integer is chosen between 0 and 100. What is the probability that it is not divisible by 7?

Cards with numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has a square number.

Box ‘A’ contains 25 slips of which 19 are marked ₹1 and other are marked ₹5 each. Box B contains 50 slips of which 45 are marked ₹1 each and others are marked ₹13 each. Slip of both boxes are poured into a third box and reshuffled. A slip is drawn at random. What is the probability that it is marked other than ₹1.

A child’s game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a square.

A child’s game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a square of blue colour.

A carton of 24 bulbs contain 6 defective bulbs and one bulb is drawn at random. If the bulb selected is defective and it is not replaced and a second bulb is selected at random from the rest, what is the probability that the second bulb is defective?

A child’s game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a triangle.

A child’s game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a triangle of red colour.

A die has six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and total scores are recorded. How many different scores are possible?

In a game, the entry fee is ₹5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she loses the entry fee.

In a game, the entry fee is ₹5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she gets just her entry fee.

A lot consists of 48 mobile phones of which 42 are good, 3 have only minor defects and 3 have major defects. Varnika will buy a phone, if it is good, but the trader will only buy a mobile, if it has no major defect. One phone is selected at random from the lot. What is probability that it is acceptable to Varnika?

Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3 respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting a sum of 3.

Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3 respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting a sum of 2.

Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3 respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting each sum of 8.

Cards with numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has an even number.

A coin is tossed 3 times. List the possible outcomes, find the probability of getting all heads.

A coin is tossed 3 times. List the possible outcomes, find the probability of getting at least two heads .

A coin is tossed two times. Find the probability of getting atmost one head.

Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3 respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting a sum of 5.

The King, Queen, and Jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is a heart.

The King, Queen, and Jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is a king.

Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.

In a game, the entry fee is ₹5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she gets double entry fee.

A die has six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and total scores are recorded. What is the probability of getting a total of 7?

A lot consists of 48 mobile phones of which 42 are good, 3 have only minor defects and 3 have major defects. Varnika will buy a phone, if it is good, but the trader will only buy a mobile, if it has no major defect. One phone is selected at random from the lot. What is probability that it is acceptable to Varnika?

A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that it is white.

A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that it is not red.

At a fete, cards bearing numbers 1 to 1000, one number on one card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that the second player wins a prize, if the first has won?

At a fete, cards bearing numbers 1 to 1000, one number on one card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that the first player wins the prize?

The formula to calculate median is:

\text { Median }=1+\frac{\left(\frac{\mathrm{n}}{2}-\mathrm{cf}\right)}{\mathrm{f}} \times \mathrm{h} \\

Which of the following statement is incorrect?

Weekly income of 600 families is tabulated below:

Which of the following expressions is correct for finding the median?

Calculate the mean of the following data by the direct method.

The mean of the below data is 35. Find the missing frequency using the direct method.

An aircraft has 120 passenger seats. The number of seats occupied during 100 flights is given in the following table :

Determine the mean number of seats occupied over the flights by the assumed mean method.

The monthly income of 100 families are given as below :

Calculate the modal income.

The maximum bowling speeds, in km per hour, of 33 players at a cricket coaching centre are given as follows:

Calculate the median bowling speed.

The weights (in kg) of 50 wrestlers are recorded in the following table:

Find the mean weight of the wrestlers by the assumed mean method.

Find the mean marks of the students for the following distribution:

The median of the following data is 50. Find the values of p and q, if sum of all the frequencies is 90.

Find the mean age of 100 residents of a town from the following data by using the step-deviation method.

The mean of following frequency distribution is 50, but the frequencies f₁ and f₂ in classes (20–40) and (60–80) respectively are not known. Find these frequencies, if the sum of all the frequencies is 120.

Determine the mean of the following distribution:

What is the formula to calculate the mean by the assumed mean method?

The weight of tea in 70 packets are shown in the following table:

Find the mean weight of packets.