. The Miami Heat are down 3 points to the Lakers at the end of a game. As the bu
ID: 3049616 • Letter: #
Question
. The Miami Heat are down 3 points to the Lakers at the end of a game. As the buzzer sounds, LeBron James (a Heat player) is fouled while attempting a three pointer. After James lands, he is pushed by an opposing player which results in a technical foul against the Lakers. A referee awards James a total of 5 free throws. Each free throw is worth one point. James’ free throw average for the season is 75%.
You may treat the free throws as independent with a 75% chance of each free throw going in. What is the probability the Heat win the game outright or force overtime? (i.e. What is the probability James makes at least 3 of his free-throws?)
Explanation / Answer
n = 5
p = 0.75
P(X = x) = 5Cx * 0.75x * (1 - 0.75)5-x
P(X > 3) = P(X = 3) + P(X = 4) + P(X = 5)
= 5C3 * 0.753 * 0.252 + 5C4 * 0.754 * 0.251 + 5C5 * 0.755 * 0.250
= 0.8965
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