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There are 30 cards, of same size, in a bag on which numbers 1 to 30 are written. One card is taken out of the bag at random.

Find the probability that the number on the selected card is not divisible by 3.

Answer:

**Solution:**

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: 30 cards of same size in a bag on which numbers 1 to 30 are written. And, one card is taken out of the bag at random.

Required to find: Probability that the number on the selected card is not divisible by 3.

Total number of possible outcomes are 30 {1, 2, 3, … 30}

Let E = event of getting a number that is divisible by 3

So, the number of favourable outcomes = 10{3, 6, 9, 12, 15, 18, 21, 24, 27, 30}

Probability, P(E) = Number of favourable outcomes/ Total number of outcomes

P(E) = 10/30

= 1/3

\overline{\mathrm{E}} \text { Then, = Event of getting number not divisible by } 3

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

= 2/3

**Thus, the probability that the number on the selected card is not divisible by 3 = 2/3**

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