Kenneth Rosen Edition 7 Exercise 6.2 Question 4 (Page No. 405)

Question

A bowl contains $10$ red balls and $10$ blue balls. A woman selects balls at random without looking at them.

• A. How many balls must she select to be sure of having at least three balls of the same color?
• B. How many balls must she select to be sure of having at least three blue balls?

Comments

If answer is correct, plz select it

Answer 1

FOR A

Using Pigeonhole Principle we she must select X ball such that ceiling(X/2) =3 So X = 2*(3-1) +1 = 5 OR

2(red)+2(blue)+1 (either blue or red)=5

FOR B

 She has to select at least 13 balls to ensure the color.

10(red)+2(blue)+1(blue)=13