6. (worth 15 points) The Washington Nationals are facing the Chicago Cubs in the

Question

6. (worth 15 points) The Washington Nationals are facing the Chicago Cubs in the first round of the playoff series. Suppose it is assumed that the probability that the Nationals will beat the Cubs in any single game is 0.6. A team wins the playoff series if it wins 3 out of 5 games. a. What is the probability that the Nationals win the series in 4 games? b. What is the probability that the Nationals will win the series? c. What is the probability that Cubs will win the series in 5 games? 7. (worth 10 points) A bank has one automatic teller machine (ATM) Customers arrive at the machine at a rate of 10 per hour. ( 10). Assuming that the number of customers, X, arrive according to a Poisson distribution, find the probability that: a. There will be exactly 7 customers in the next hour. (P(X = 7)) b. There will be between 8 and 11 customers in the next hour. (R(8

Explanation / Answer

P(National winning ) = 0.6

Ans 6

a) P( Nationals will win 3 out of 4 games ) = 0.6^3*0.4 = 0.0864

b)P(Nations will win the series ) = P(Nationals win 3 games out of 5)+ P(Nationals win 3 games out of 5)+ P(Nationals win 3 games out of 5)

= 0.6^3*0.4^2+0.6^4*0.4+0.6^5 = 0.16416

c)  P( cubs will win 3 out of 5 games ) = 0.6^2*0.4 ^3= 0.02304

Ans7

a) Poisson Probability: P(X = 7) = 0.09

b) P(8<x<11) = P(x<11)-P(x<=8)

Poisson Probability: P(X = 11) = 0.1137

Cumulative Probability: P(X < 8) = 0.332

P(8<x<11) =  0.332-0.1137

= 0.2183

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