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Problems Geometry Plane geometry Area Area ratio Area ratio (other) Probability and statistics Probability theory Conditional probability Continuous distribution

13–16 4.0

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?

Problem #PRU-65305

Problems Geometry Plane geometry Area Area of a circle, sector, segment Probability and statistics Probability theory Continuous distribution Algebra Mean values

13–16 3.0

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.