Question

it is computed that when a basketball player shoots a free - throw, the odds in favor of his making it are 21 to 3. 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{1}{8}) (type an integer or a simplified fraction.) the player should make out of 100 free throws. (round to the nearest integer as needed)

Explanation:

Step1: Recall probability - odds relationship

The odds in favor of an event $E$ is given by $\text{Odds}=\frac{P(E)}{1 - P(E)}$. Here, odds in favor of making a free - throw is $\frac{21}{3}=7$. Let $P$ be the probability of making a free - throw. So, $\frac{P}{1 - P}=7$.

Step2: Solve for the probability of making a free - throw

Cross - multiply: $P = 7(1 - P)$. Expand: $P=7 - 7P$. Add $7P$ to both sides: $P + 7P=7$, so $8P = 7$, and $P=\frac{7}{8}$. Then the probability of missing a free - throw is $1 - P=1-\frac{7}{8}=\frac{1}{8}$.

Step3: Find the number of free - throws made out of 100

If the probability of making a free - throw is $P=\frac{7}{8}$, and the number of attempts $n = 100$. The expected number of made free - throws is $n\times P$. So, $100\times\frac{7}{8}=\frac{700}{8}=87.5\approx88$.

Answer:

The probability that the player misses the free throw is $\frac{1}{8}$.
The player should make 88 out of 100 free throws.