Question

A bag contains cards which are numbered from 5 to 100, such that each card bears a different number. A card is drawn at random. Find the probability that the number on the card is:

1. a perfect square.
2. a 2-digit number.

Answer 1

S = {5, 6, 7, 8, ..., 100}

Total cards n(S) = 96

i. Perfect square (A) = {9, 16, 25, 36, 49, 64, 81, 100}

n(A) = 8

P(Perfect square) = `(n(A))/(n(S))`

= `8/96`

= `1/12`

ii. A two-digit number = {10, 11, 12, ..., 99}

Total = 90

P(two-digit number) = `90/96`

= `30/32`

= `15/16`