Question

A box contains cards bearing numbers 6 to 70. If one card is drawn at random from the box, find the probability that it bears a composite number between 50 and 70.

Answer 1

Let E₄ be the event of getting a composite number between 50 and 70.

Out of these numbers, composite numbers between 50 and 70 are 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68 and 69.

Number of favourable outcomes = 15.

∴ P(getting a composite number between 50 and 70) = P(E₄) = `("Number of outcomes favourable to" E_2)/"Number of all possible outcomes"` 

`= 15/65=3/13` 

Thus, the probability that the card bears a composite number between 50 and 70 is `3/13`.