A basketball player makes 75% of the free throws that he attempts. What is the probability, approximated, that he succeeds in half of them in 40 tries?
The probability that the basketball player succeeds in half of the 40 free throws is approximately 0.44.
To find the probability that the basketball player succeeds in half of the free throws in 40 tries, we can use the binomial distribution formula.
The formula for the binomial distribution is:
P(x) = C(n, x) * p^x * (1 - p)^(n - x)
Where:
P(x) is the probability of getting exactly x successes,
C(n, x) is the number of ways to choose x successes from n trials,
p is the probability of success in a single trial, and
n is the number of trials.
In this case, the basketball player makes 75% of the free throws, so the probability of success in a single trial (p) is 0.75. The player attempts 40 throws (n), and we want to find the probability of getting exactly half of them, which is 20 successes (x). Therefore, we can plug these values into the binomial distribution formula.
P(x = 20) = C(40, 20) * 0.75^20 * (1 - 0.75)^(40 - 20)
Using a calculator or statistical software, we can calculate this probability approximately.
To determine the probability that a basketball player succeeds in half of the free throws in 40 attempts, we can use the binomial probability formula.
The binomial probability formula is given by:
P(x) = (nCx)*(p^x)*((1-p)^(n-x))
Where:
- P(x) is the probability of getting exactly x "successes"
- n is the number of trials or attempts
- x is the number of successful outcomes we are interested in
- p is the probability of a single success
In this case, the basketball player makes 75% of the free throws, so the probability of a single success (making a free throw) is 75% or 0.75. The player attempts 40 free throws, and we want to know the probability of succeeding in exactly half of them, which is 20.
Substituting the values in the formula, we get:
P(20) = (40C20)*(0.75^20)*((1-0.75)^(40-20))
To solve this, we need to calculate the values of (40C20) which represents the number of ways to choose 20 items from a set of 40, and then evaluate the remaining formula.
Using a calculator or statistical software, we find that (40C20) is approximately 137,846.
Now, we can plug in the values:
P(20) = 137,846 * (0.75^20) * (0.25^20)
Evaluating this expression, we find that the probability, approximated, that the basketball player succeeds in half of the free throws in 40 tries is approximately 0.0354 or 3.54%.