Question:
The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is
(a) $\frac{4}{15}$
(b) $\frac{2}{15}$
(c) $\frac{1}{5}$
(d) $\frac{1}{3}$
Solution:
Total number of outcomes = 15.
Out of the given numbers, multiples of 4 are 4, 8 and 12.
Numbers of favourable outcomes = 3.
$\therefore \mathrm{P}($ getting a multiple of 4$)=\frac{\text { Number of favourable outcomes }}{\text { Number of all possible outcomes }}$
$=\frac{3}{15}=\frac{1}{5}$
Thus, the probability that a number selected is a multiple of 4 is $\frac{1}{5}$.
Hence, the correct answer is option (c).
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