Question

Cards bearing numbers 1,2,5,….,35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing (i) a prime number less than 15, (ii) a number divisible by 3 and 5. Select the correct answer from above options

Answer 1

Correct Answer - ` (i) 5/18 (ii) 1/9` The numbers 1,3,5,…35 form an AP with a = 1 and d = 2. Let `T_(n) = 35`. Then, ` 1+(n-1) xx 2 = 35 rArr (n-1) xx 2 = 34 rArr n - 1 = 17 rArr n = 18`. ` :. ` number of all possible outcomes = 18. (i) Out of the given numbers, the prime numbers less than 15 are 3,5,7,11,13. Their numbers is 5. ` :.` P(getting a prime numbers)=` 5/18`. (ii) A number is divisible by 3 and 5 means, it must be divisible by 15. The numbers divisible by 15 are 15 and 30. Their numbers is 2. ` :. ` P(getting a numbers divisible by both 3 and 5) `=2/18 = 1/9`.