Problem #PRU-65784

Problems Probability and statistics Probability theory Continuous distribution

Problem

One day in autumn the Scattered Scientist glanced at his ancient wall clock and saw that three flies fell asleep on the dial. The first one slept exactly at the 12 o’clock mark on the clock, and the other two just as neatly settled on the marks of 2 hours and 5 hours. The scientist made measurements and determined that the hour hand does not threaten the flies, but the minute one will sweep them all in turn. Find the probability that exactly 40 minutes after the Scientist noticed the flies, exactly two flies out of three were swept away by the minute hand.