The percentage of wins for the Dallas Mavericks NBA basketball team in the playo
ID: 3151133 • 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
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.
Probability of WIN for Dallas Mavericks (DM) against Golden State Warriors (GSW) = 0.4
Probability of LOSS for Dallas Mavericks (DM) against Golden State Warriors (GSW) = ( 1 - 0.4 ) = 0.6
(A)
For Mavs to sweep GSW (4-0, i.e. 4 wins, 0 losses) .Mavericks have to win first 4 matches played against GSW in the round one playoff series.
Probability of Mavericks winning first 4 matches against GSW in 1st round of playoff series
= Probability of WIN for (DM) against (GSW) * Probability of WIN for (DM) against (GSW) * Probability of WIN for (DM) against (GSW) * Probability of WIN for (DM) against (GSW)
= 0.4 * 0.4 * 0.4 * 0.4
= 0.0256
.
(B)
For the Mavs win the initial best-of-7 playoff series 4 - 0
Probability = 0.4 * 0.4 * 0.4 * 0.4 = 0.0256 (As solved above)
For the Mavs win the initial best-of-7 playoff series 4 - 1
Probability = Probability of DM win against GSW in first 4 matches * Probability of DM loss against GSW in last match
= 0.4 * 0.4 * 0.4 * 0.4 * 0.6
= 0.01536
For the Mavs win the initial best-of-7 playoff series 4 - 2
Probability = Probability of DM win against GSW in first 4 matches * Probability of DM loss against GSW in last 2 matches
= 0.4 * 0.4 * 0.4 * 0.4 * 0.6 * 0.6
= 0.009216
For the Mavs win the initial best-of-7 playoff series 4 - 3
Probability = Probability of DM win against GSW in first 4 matches * Probability of DM loss against GSW in last 3 matches
= 0.4 * 0.4 * 0.4 * 0.4 * 0.6 * 0.6 * 0.6
= 0.0055296
So,
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)
= Probability that the Mavs win the initial best-of-7 (4-0) + Probability that the Mavs win the initial best-of-7 (4-1) + Probability that the Mavs win the initial best-of-7 (4-2) + Probability that the Mavs win the initial best-of-7 (4-3)
= 0.0256 + 0.01536 + 0.009216 + 0.0055296
= 0.0557056
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