Question

it is computed that when a basketball player shoots a free throw, the odds in favor of his making it are 23 to 5. find the probability that when this basketball player shoots a free throw, he misses it. out of every 100 free throws he attempts, on the average how many should he make? the probability that the player misses the free throw is \boxed{}. (type an integer or a simplified fraction.)

Explanation:

Step1: Recall the formula for probability from odds

If the odds in favor of an event \(E\) are \(a:b\), then \(P(E)=\frac{a}{a + b}\). Here, the odds in favor of making the free - throw are \(23:5\). So the probability of making the free - throw \(P(\text{make})=\frac{23}{23 + 5}=\frac{23}{28}\).

Step2: Use the complement rule

The probability of an event \(E\) and its complement \(\overline{E}\) (not \(E\)) satisfy \(P(E)+P(\overline{E}) = 1\). Let \(E\) be the event of making the free - throw. Then the probability of missing the free - throw \(P(\text{miss})=1 - P(\text{make})\).
Substitute \(P(\text{make})=\frac{23}{28}\) into the formula: \(P(\text{miss})=1-\frac{23}{28}=\frac{28 - 23}{28}=\frac{5}{28}\).

Answer:

\(\frac{5}{28}\)