A box contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the drawn card is (i) divisible by 2 or 3, (ii) a prime number.

Question

Philoid · Accepted Answer

Total numbers of elementary events are 25

(i) Let E be the event of drawing number divisible by 2 or 3

Let A be the event of drawing number divisible by 2

The favourable numbers are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

Then, numbers of favourable outcomes are: 12

P (number divisible by 2) = P (A) = 12/25

Let B be the event of drawing a number divisible by 3

The favourable numbers are: 3, 6, 9, 12, 15, 18, 21, 24

Then, numbers of favourable outcomes are: 8

P (getting number divisible by 3) = P (B) = 8/25

∴ P (number divisible by 2 or 3) = P (A) + P (B) = 12/25 + 8/25 = 20/25 = 4/5

(ii) Let E be the event of drawing a prime number

The favourable numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23

Then, numbers are favourable outcome are: 9

∴ P (prime number) = P (E) = 9/25