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.

Answer

` (i) 3/17 (ii) 7/51`

Explanation

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`.