Question

Cards marked with numbers 1,3,5,…101 are placed in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that a number on the drawn card is (i) less than 19, (ii) a prime number less than 20. Select the correct answer from above options

Answer 1

Correct Answer - ` (i) 3/17 (ii) 7/51` Given numbers 1,3,5,…,101 form an AP with a =1 and d =2. Let ` T_(n) = 101`. Then, `1+(n-1)xx2 = 101 rArr (n-1) xx 2 = 100 rArr n -1 = 50 rArr n = 51`. ` :.` total number of cards = 51. (i) Out of the given numbers, those less than 19 are 1,3,5,...,17. Let `t_(m) = 17`. Then,` 1+(m-1) xx 2 = 17 rArr (m-1) xx 2 = 16 rArr m -1 = 8 rArr m = 9`. ` :. ` P(getting a number less than 19) ` = 9/51 = 3/17`. (ii) Out of the given numbers, the prime numbers less than 20 are 3,5,7,11,17,19. Their number is 7. ` :. ` P(getting a prime number less than 20) ` = 7/51`.