The percentage of wins for the Dallas Mavericks NBA basketball team in the playo
ID: 3150235 • Letter: T
Question
The percentage of wins for the Dallas Mavericks NBA basketball team in the playoffs this season is assumed to be 40% against Golden State Warriors, since GSW has Steph Curry, the 2015 MVP, on the roster. Let’s assume that this probability will persist during the first round of the playoffs (the side which wins the best-of-7 wins the first round of the series) against the GSW. (a) What is the probability that the Mavs sweep (4-0, i.e. 4 wins, 0 losses) the round one playoff series? (b) What is the probability that the Mavs win the initial best-of-7 playoff series in any way they can (i.e. 4-0, or 4-1, or 4-2, or 4-3)?
Explanation / Answer
(a) What is the probability that the Mavs sweep (4-0, i.e. 4 wins, 0 losses) the round one playoff series?
That means they win 4 out of 4 games.
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 4
p = the probability of a success = 0.4
x = the number of successes = 4
Thus, the probability is
P ( 4 ) = 0.0256 [ANSWER]
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(b) What is the probability that the Mavs win the initial best-of-7 playoff series in any way they can (i.e. 4-0, or 4-1, or 4-2, or 4-3)?
Thus, they have to win at least 4 games out of 7.
Note that P(at least x) = 1 - P(at most x - 1).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 7
p = the probability of a success = 0.4
x = our critical value of successes = 4
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 3 ) = 0.710208
Thus, the probability of at least 4 successes is
P(at least 4 ) = 0.289792 [ANSWER]
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