a box contains cards numbered 3,5,7,9...,35,37. A card is drawn at random from the box. Find the probability that the numbe on the drawn card is a prime number

the primes in the sequence are

3,5,7,11,13,17,19,23,29,31,37

which are 11 in total

no of cards is 17

so, 

probability of getting a prime is 

11/17

using  AP

An = 37

A = 3

D = 2

An =  A + ( n- 1 ) D 

37 = 3 + ( n-1) 2

34 = 2n - 2

36 = 2n

18 = n

so, there are 18 cards

prime in odd numbers from 3 - 37 = 3 , 5 , 7 , 11, 13, 17, 19 , 23, 29, 31, 37

= 11 favourable outcomes

probability = 11/ 18

total no. of cards = 18

no. of cards containimg prime no.s = 11

P(E) of getting prime no. = no. of cards containing prime no.s / total no. of cards

                                            = 11 / 18