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 $\le$ 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 number of times in a period of 12 hours the hands of the clock 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 number of times when the hands are alligned ( $0^{\circ }$), hands are at right angles and hands are facing in opposite directions ( ${180}^{\circ }$), then the probability would be slightly less than 0.5.