6. Stopped Clock (from 6th grade. 1 point). On the clock, there are two hands: the hour hand and the minute hand. At a random moment in time, the clock stopped. Find the probability that the angle between the hands on the stopped clock is acute.
Solution. Suppose the clock face also rotates at the speed of the hour hand so that the hour hand always points to 12 o'clock. Then the minute hand will form an acute angle if it is in the interval from 12 to 3 o'clock or from 9 o'clock to 12, that is, within six of the twelve hour intervals. The desired probability is $\frac{6}{12}=\frac{1}{2}$.

Answer: 0.5.