If the probability that the Islanders will beat the Rangers in a game is 85%, what is the probability that the Islanders will win exactly three out of five games in a series against the Rangers? Round your answer to the nearest thousandth.
5 answers
3(.85) + 2(.15) = ?
The probability of an event, p, occurring exactly r times:
n Cr * p^r * q^(n-r)
Binomial Probability-1
n = number of trials
r = number of specific events you wish to obtain
p = probability that the event will occur
q = probability that the event will not occur
(q = 1 – p, the complement of the event)
n Cr * p^r * q^(n-r)
Binomial Probability-1
n = number of trials
r = number of specific events you wish to obtain
p = probability that the event will occur
q = probability that the event will not occur
(q = 1 – p, the complement of the event)
p = .85
q = .15
n = 5
r = 3
C(n,r) = n!/ [ r!(n-r)! ] = 5!/[ 3!( 2!) ] = 5 *4 /2 = 10
so
10 * .85^3 * .15^2
= 0.138
q = .15
n = 5
r = 3
C(n,r) = n!/ [ r!(n-r)! ] = 5!/[ 3!( 2!) ] = 5 *4 /2 = 10
so
10 * .85^3 * .15^2
= 0.138
2 ways to interpret the question:
1. There are actually 5 games
2. What is the prob that the Islanders win 3 games to win the series.
1. In the 5 games for the Islanders to win the series, the last game must
be a win, W, the other 4 games must be permutations of WWLL
---- there are 4!/(2!2!) or 6 of these
Prob(Islanders win in exactly 5 games) = 6(.85)^3 (.15)^2 = .0829
2. Possible ways to win series Islanders can win:
a) win in 3 straight --- .85^3 = .614125
b)) win in 4 games, there are 3 such cases, only 1 loss, one is WWLW
prob(to win in 4 games) = 3(.85)^3(.15) = .27636
c) win in 5 games, see above 1)
prob(t win in 5 games) = .0825
prob(islander win the series ) = .614125 + .27636 + .0825 = .973
(notice that this does not add up to 1, since there is a chance
the Islanders could lose the series)
1. There are actually 5 games
2. What is the prob that the Islanders win 3 games to win the series.
1. In the 5 games for the Islanders to win the series, the last game must
be a win, W, the other 4 games must be permutations of WWLL
---- there are 4!/(2!2!) or 6 of these
Prob(Islanders win in exactly 5 games) = 6(.85)^3 (.15)^2 = .0829
2. Possible ways to win series Islanders can win:
a) win in 3 straight --- .85^3 = .614125
b)) win in 4 games, there are 3 such cases, only 1 loss, one is WWLW
prob(to win in 4 games) = 3(.85)^3(.15) = .27636
c) win in 5 games, see above 1)
prob(t win in 5 games) = .0825
prob(islander win the series ) = .614125 + .27636 + .0825 = .973
(notice that this does not add up to 1, since there is a chance
the Islanders could lose the series)
I am going to scream.