Question

cards marked with numbers 5 to 100 are placed.one card is drawn from this . find the probblity that the no. on the card is
1) a perfect square
2) a multiple of 7
3 ) a prime no. less than 25

Answer 1

We have totally  100-5+1 = 96 cards in the pack.

Perfect squares between 5 and 100 are :
   9, 16, 25, 36, 49, 64, 81, 100  => there are 8 of them.

1) Probability that a randomly drawn card from the pack is a perfect square is
         8/96 = 1/12

2) Multiples of 7 between 5 and 100:
         7 * 1 to  7 * 14      => there are 14 cards.
    Probability that a randomly drawn card is numbered with a multiple of seven:
         14/96 = 7/48

3) Prime numbers < 25 are :
       2, 3, 5, 7, 11, 13, 17, 19, 23 :  so probability = 9/96 = 3/32

Answer 2

Probability= number of favourable events /total no.of events or possibilities......In this case the total no. Of events are 96(total no. Of cards).... No. Of perfect square no between 5 and 100 is 8.(9,16,25,36,49,64,81,100)....,Thereof the probability for 1) is 8/96 or 1/12....the no.of multiples of 7 till 100 is 14(use table I.e 7*14=98)..the probability for 2) is 14/96 or 7/48...No.Of prime numbers less than 25 is 7 ( starting from 5..,,..5,7,11,13 ,17,19,23) thereof the probability for 3) is 7/96