A bag contains 16 cards bearing numbers 1, 2, 3, ..., 16 respectively. One card is chosen at random.
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) $\frac{13}{16}$
Solution:
(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.
$\therefore$ Required probability $=P(E)=\frac{5}{16}$
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