Question

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

Options

• P > 0.5

• P = 0.5

• P < 0.5

• P ≤ 0.25

Answer 1

P < 0.5

Explanation:

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 12. But if you take into account the small amounts of time when the hands are aligned ( 0^∘), hands are at right angles and hands are facing in opposite directions (180^∘), then the probability would be slightly less than 0.5.