Kate and Gina agreed to meet at the underground in the first hour of the afternoon. Kate comes to the meeting place between noon and one o’clock in the afternoon, waits for 10 minutes and then leaves. Gina does the same.
a) What is the probability that they will meet?
b) How will the probability of a meeting change if Gina decides to come earlier than half past twelve, and Kate still decides to come between noon and one o’clock?
c) How will the probability of a meeting change if Gina decides to come at an arbitrary time between 12:00 and 12:50, and Kate still comes between 12:00 and 13:00?
The upper side of a piece of square paper is white, and the lower one is red. In the square, a point F is randomly chosen. Then the square is bent so that one randomly selected vertex overlaps the point F. Find the mathematical expectation of the number of sides of the red polygon that appears.
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.