Question

The probability of a basketball player making a free throw during the regular season is 5/6. During a championship game, this player made two out of three attempts. Based on his regular season record, what was the probability of making two out of three attempts?

Answer 1

The probability of making two out of three attempts based on the regular season record is 25/72.

Step-by-step explanation:

To find the probability of making two out of three attempts based on the regular season record, we need to calculate the probability of making exactly two shots and the probability of missing one shot. The probability of making each individual shot in the regular season is 5/6. The probability of missing a shot is therefore 1 - 5/6 = 1/6.

To calculate the probability of making two shots and missing one shot, we use the binomial probability formula: P(X=k) = nCk * p^k * (1-p)^(n-k)

In this case, n=3 (total number of attempts), k=2 (number of successful attempts), p=5/6 (probability of success), and 1-p=1/6 (probability of failure).

Plugging these values into the formula, we get: P(X=2) = 3C2 * (5/6)^2 * (1/6)^(3-2) = 3 * (25/36) * (1/6) = 75/216 = 25/72. Therefore, the probability of making two out of three attempts based on the regular season record is 25/72.