It is computed that when a basketball player shoots a free throw, the odds in favor of his making it are 23 to 6 . 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 $\frac{6}{29}$. (Type an integer or a simplified fraction.) The player should make 100 free throws. (Round to the nearest integer as needed.)
Solution
Step 1 ：The odds in favor of the player making a free throw are given as 23 to 6. This means that for every 29 attempts (23+6), the player makes 23 and misses 6.
Step 2 ：Therefore, the probability of missing a free throw is the number of misses divided by the total number of attempts. So, the probability that the player misses the free throw is \(\frac{6}{29}\).
Step 3 ：We need to find out how many free throws the player should make out of 100 attempts on average. This can be calculated by multiplying the probability of making a free throw by 100.
Step 4 ：So, the player should make approximately 79 free throws out of every 100 attempts.
Step 5 ：\(\boxed{\text{The probability that the player misses a free throw is }\frac{6}{29}\text{ and he should make approximately 79 free throws out of every 100 attempts.}}\)
