Question

A box contains 1to 100 number cards. If one card is drawn at random find the probability of that card will be 1) perfect square 2) a prime number
3 ) a two digit number 4) a multiple of 9

Answer 1

Step-by-step explanation:

Let 'S' be the sample space

n(S)=100

1) Let 'A' be the event of selecting a perfect square card

A={1, 4, 9, 16, 25, 36, 49, 64, 81, 100}

n(S)=10

P(A)=n(A)/n(S)

=10/100

=1/10

2)Let 'B' be the event of selecting a prime number card

B={2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}

n(B)=25

P(B)=n(B)/n(S)

=25/100

=1/4

3)Let 'C' be the event of selecting a two digit card

n(C)=90

P(C)=n(C)/n(S)

90/100

=9/10

4)Let 'D' be the event of selecting a 9 multiple card

D={9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99}

n(D)=11

P(D)=n(D)/n(S)

=11/100