Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner

Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner


H
Asked by 2 years ago
240 points

Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner. Suppose that one of the teams is stronger than the other and wins each game with probability .6, independently of the outcomes of the other games. Find the probability, for i = 4, 5, 6, 7, that the stronger team wins the series in exactly i games. Compare the probability that the stronger team wins with the probability that it would win a 2-out of-3 series.

Two athletic
hansel

2 Answers

Answered by 2 years ago
8.7k points

First the probability of winning in 4 games is given by,

$$(0.6)^4$$

now for i = 5,6,7 (look up negative binomial),

$$P(\text{win in i games})=(C(i,4)-C(i-1,4))(0.6)^4(1-0.6)^{i-4}=C(i-1,3)(0.6)^4(0.4)^{i-4}$$

and for 2 out of 3,

$$P(\text{2 out of 3})=(C(3,2)-C(2,2))(0.6)^2(0.4)^1$$

R
Answered by 1 year ago
0 points

Oh Snap! This Answer is Locked

Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner

Thumbnail of first page

Excerpt from file: Organic Vita-Hair Marketing Portfolio 1 ORGANICVITAHAIRMARKETINGPORTFOLIO EXECUTIVE SUMMARY OrganicVitaHaircamefromhumblebeginnings,buttheownersawaclearvisionahead ofherasshebegantoexpandhershampooproductintoalargerproductlineincludingbeauty

Filename: MKT 500 Assignment 5 Marketing Strategies.docx

Filesize: < 2 MB

Downloads: 0

Print Length: 22 Pages/Slides

Words: 476

Your Answer

Surround your text in *italics* or **bold**, to write a math equation use, for example, $x^2+2x+1=0$ or $$\beta^2-1=0$$

Use LaTeX to type formulas and markdown to format text. See example.

Sign up or Log in

  • Answer the question above my logging into the following networks
Sign in
Sign in
Sign in

Post as a guest

  • Your email will not be shared or posted anywhere on our site
  •  

Stats
Views: 99
Asked: 2 years ago

Related