Use the pigeonhole principle to answer the following questions. Give an explanat

Question

Use the pigeonhole principle to answer the following questions. Give an explanation of how you arrived at your answer. A box contains 8 red balls and 8 black balls. A woman takes balls out at random without looking at them. Once a ball is taken out it is not replaced back in the box. How many balls must she select to be sure of having at least three balls of the same color? How many numbers must be selected from the set{1,2,3,4,5,6,7,8} to guarantee that at least one pair of these numbers add up to exactly 9?

Explanation / Answer

Given that

A box contains red balls=8

Black balls=8

Given that randomly the balls are taken out

The propabitly is(1/8) for one ball

The ball is not replaced hence 1/8

Given that 3 balls are of same color at least

Therefore the 3 balls selected from 8 balls of one color=(3/8)

Same thefeore 2 colors are present= {3/8}+{3/8}

Having same color the probability =(6/8)=[3/4]

b.,given set of numbers{1,2,3,4,5,6,7,8,9}

The numbers add exactly 9=?

Therefore the set should be partornized as sets

{1,8}

{2,7}

{3,6}

{4,5}

Therefore to get atleast one pair of these numbers add up to exactly 9.

8 numbers gets exactly 9

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.