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Question
Cards bearing numbers 1, 3, 5, .... , 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing a number divisible by 3 and 5.
Solution
Given number 1, 3, 5, .... , 35 form an AP with a = 1 and d = 2.
Let Tn = 35. Then,
1 + (n − 1)2 = 35
⇒ 1 + 2n − 2 = 35
⇒ 2n = 36
⇒ n = 18
Thus, total number of outcomes = 18.
Let E2 be the event of getting a number divisible by 3 and 5.
Out of these numbers, number divisible by 3 and 5 means number divisible by 15 is 15.
Number of favourable outcomes = 1.
∴ P(getting a number divisible by 3 and 5) = P(E2) = `("Number of outcomes favourable to" E_2)/"Number of all possible outcomes"`
`= 1/18`
Thus, the probability of getting a card bearing a number divisible by 3 and 5 is `1/18`.
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