RD Sharma Solutions Class 10 Mathematics Solutions for Probability Exercise 13.1 in Chapter 13 - Probability

Question 46 Probability Exercise 13.1

A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is not black.



When one event happens if and only if the other one doesn't, two occurrences are said to be complimentary. The probability of two complementary events add up to one.

Given: A bag contains 7 red, 5 black and 3 white balls and a ball is drawn at random

Required to find: Probability of getting a Not black ball

Total number of balls 7 + 5 + 3 = 15

Total number of black balls is 5

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of drawing black ball P(E) = 5/15 = 1/3

But, this is not what is required.

And, we know that sum of probability of occurrence of an event and probability of non-occurrence of an event is 1

\begin{aligned} &P(E)+P(\bar{E})=1 \\ &\frac{1}{3}+P(\bar{E})=1 \\ &P(\bar{E})=1-\frac{1}{3} \\ &P(\bar{E})=\frac{2}{3} \end{aligned}

Thus, the probability of drawing a ball that is not black is 2/3

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