Question

100 cards marked from 2 to 101 are placed in a box and mixed thoroughly. One card is drawn at random

from the box. Find the probability that number on the card is

(i) an even number

(ii) a number which is a perfect square

(iii) a prime number less than 20​

Answer 1

There are 100 cards in the box out of which one card can be drawn in 100 ways.

Total number of elementary events=100

a)From no.s 2 to 101,there are 50 even no.s.

Favourable no. of elementary events=50

P(getting an even no. card)=50/100=1/2

b)There are 12 cards bearing no.s less than 14.

Favourable no. of elementary events=12

P(getting a no. less than 14)=12/100=3/25

c)Those no.s from 2 to 101 which are perfect squares are 4,9,16,25,.......,100 i.e. squares of 2,3,4,5,.......,10 respectively.Therefore there are 9 cardsmarked with the no.s which are perfect squares.

Favourable no. of elementary events=9

P(getting a no. which is a perfect square)=9/100

d)Prime no.s less than 20 in the no.s from 2 to 101 are 2,3,5,7,11,13,17 and 19.

Thus,there are 8 cards marked with prime no.s less than 20.

Favourable no. of elementary events=8

P(getting a prime no. less than 20)=8/100=2/25.

Answer 2

i) p(e) = no.of observation/total no of observation

= 50/100

=1/2

ii) p(e) = 12/100

= 3/25

iii) p(e) = 8/100

= 2/25