Question

What is the probability that the minute and hour hands of a clock will form an acute angle at any given time?

• A. P <= 0.25
• B. P < 0.5
• C. P = 0.5
• D. P > 0.5

Answer 1

The correct option is B

P < 0.5

The amount of time in a period of 12 hours when the hands will form an acute angle will be the same as that for obtuse angle. So, you would think that the probability is $\frac{1}{2}$. But if you take into account the small amounts of time when the hands are aligned ( $0^{\circ }$), hands are at right angles and hands are facing in opposite directions ( ${180}^{\circ }$), then the probability would be slightly less than 0.5.