Question

a bowl contains 10 red balls and 10 blue balls. a woman selects balls at random without looking at them. ch 06 sec 2 ex 04 (a) - pigeonhole principle how many balls must she select to be sure of having at least three balls of the same color?

Answer 1

To be sure of having at least three balls of the same color, she must select at least 12 balls.

Step-by-step explanation:

The pigeonhole principle states that if there are n+1 pigeons and n pigeonholes, then at least one pigeonhole must contain more than one pigeon.

In this case, there are 10 red balls and 10 blue balls, so there are a total of 20 balls. To ensure that at least three balls are of the same color, we need to consider the worst-case scenario, which is selecting all 10 red balls and the first 2 blue balls. This would make a total of 12 balls.

Therefore, she must select at least 12 balls to be sure of having at least three balls of the same color.