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 \\(\frac{5}{28}\\).
(type an integer or a simplified fraction.)
the player should make \\(\square\\) out of 100 free throws.
(round to the nearest integer as needed.)

Explanation:

Step1: Find the probability of making a free - throw

If the odds in favor of making a free - throw are \(23\) to \(5\), then the probability of making a free - throw \(P(\text{make})\) is given by the formula \(P(\text{make})=\frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}\). The total number of outcomes is \(23 + 5=28\). So \(P(\text{make})=\frac{23}{28}\).

Step2: Calculate the number of free - throws made out of 100

We use the formula \(n = N\times P\), where \(N = 100\) (the total number of free - throws) and \(P=\frac{23}{28}\) (the probability of making a free - throw). Then \(n=100\times\frac{23}{28}=\frac{2300}{28}\approx82.14\).

Answer:

\(82\)