The Indians and Yankees are to face each other in a best two out of three playoff series. The probability of the Indians winning any given game is 0.3%
A. what is the prob. that the Indians win the second game? B. What is the probability that the Indians win the second game given that they won the first game? Lost the first game? C. what is the probability that the Indians win the series? D. What is the probability the Indians win the series given that they won the first game? Lost the first game? E.What is the prob. that the Yankees win the first two games? that the Indians win the first two games? F. What is the probability the series goes to three games?
A. independent events so 0.3
B. 0.3
C.
we want the sum of the probabilities that Indians win 2 games
That can happen several ways
1 1
1 0 1
0 1 1
first 1 1
.3*.3 = .09
now 1 0 1
.3*.7*.3 = .063
then 0 1 1
.7*.3*.3 = .063
sum = .216 answer to C.
for a check, see how the yankees do
.7*.7 = .49
.7*.3*.7 = .147
.3*.7*.7 = .147
sum = .784
total probability that one of the teams wins = .216+.784 = 1 check
D. they must win 2 or lose2 win 3
win #2 = .3
lose #2, win #3 = .7*.3 = .21
sum = .51
you can do the win both #2 and #3 = .09
E. .7*.7 = .49
.3*.3 = .09
F. 1 - probability that yankees win first two or indians win first two
1 - .49 - .09 = .42