Each game you play is a win with probability p =0.61. You play five games but if

Question

Each game you play is a win with probability p =0.61. You play five games but if you win the fifth game then you will keep playing until you lose.

What is the probability that you win the fifth game?

a) What is the probability that you win three games in the 1st five games?

b) What is the probability that you win 3 games in the first 5 games and the third win is on the fifth game?

c) You win a game with a probability p. Find the expected number of games that you play.

d) You win a game with a probability p. Find the expected number of games that lose.

Explanation / Answer

wininig probability p =0.61 so

probability of that winning of fifth game=0.61

(a) here we use binomial distribution with parameter n=5 and p=0.61 and for

Binomial distribution ,P(X=r)=nCrpr(1-p)n-r  

probability that you win three games in the 1st five games=P(X=3)=0.3452

( using ms-excel=BINOMDIST(3,5,0.61,0))

(b) fift game is win and its probability=0.61, so remaining out of 4 game winning of 2 is calculated by  binomial distribution with parameter n=4 and p=0.61

P(X=2)=0.3396 ( =BINOMDIST(2,4,0.61,0))

(c)

(d) Find the expected number of games that lose=n(1-p)

if n is the number of games played

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