Question

A bag contains 16 cards bearing numbers 1, 2, 3, ..., 16 respectively. One card is chosen at random. What is the probability that the chosen card bears a number divisible by 3?
(a) $\frac{3}{16}$

(b) $\frac{5}{16}$

(c) $\frac{11}{16}$

(d) $\frac{13}{16}$

Answer 1

(b) $\frac{5}{16}$

Explanation:
Total number of cards in the bag = 16
Numbers on the cards that are divisible by 3 are 3, 6, 9, 12 and 15.

Number of cards with numbers divisible by 3 = 5

​Let E be the event that the chosen card bears a number divisible by 3.

∴ Required probability = P(E) = $\frac{5}{16}$