Standing at the line.

Level 2

The probability that a basketball player makes 7 out of 10 free throws is exactly the same that she makes 8 out of 10 free throws. Assuming that the probability that she makes each free throw is constant and greater than zero, find the probability that she makes her next free throw correct to three decimal places.

The answer is 0.727.

1 solution

Mark Jones
Dec 5, 2017

The probability that she makes seven of ten free throws is $\binom{10}{7}p^{7}(1 - p)^{3}$ . The probability that she makes eight of ten free throws is $\binom{10}{8}p^{8}(1 - p)^{2}$ . $120p^{7}(1 - p)^{3} = 45p^{8}(1 - p)^{2}$ . Dividing both sides by $15p^{7}(1 - p)^{2}$ gives 8(1 - p) = 3p. 8 - 8p = 3p. 8 = 11p. $p = \frac{8}{11}$ , or approximately 0.727.

Standing at the line.

The answer is 0.727.

1 solution

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