SEC16 1 A bowl contains 9 red balls and 9 blue balls A woman

SEC16) #1

A bowl contains 9 red balls and 9 blue balls. A woman selects balls at random without looking at them. How many balls must she select (minimum) to be sure of having at least three blue balls? How many balls must she select (minimum) to be sure of having at least three balls of the same color?

Solution

Solution:

a) In the worst case she may pick all 10 red balls first. Then next three blue balls.

9+3=12.

Answer:12

b) we have p = 2 bins (pigeonholes) and r = 3: the minimum number of balls (pigeons) in any of the bins. By the generalized pigeonhole principle, the answer is p(r1) + 1 = 2(3-1)+1=5

The pigeon hole principal says if you put 5 objects into 2 bins(colors) one box must contain at least 3.

Answer : 5