Answer:
The probability that Joe Biden makes his fifth shot on his eighth attempt is approximately 0.2013 or 20.13%.
Explanation:
To find the probability that Joe Biden makes his fifth shot on his eighth attempt, we can use the binomial probability formula. In this case, Joe Biden is attempting free throws, and each attempt has two possible outcomes: he either makes the shot (success) with a probability of 80% or misses the shot (failure) with a probability of 20%.
The binomial probability formula is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
where:
- P(X = k) is the probability of getting exactly k successes in n trials.
- C(n, k) is the combination (n choose k) of n items taken k at a time, which is given by C(n, k) = n! / (k! * (n - k)!).
- p is the probability of success on a single trial.
- (1 - p) is the probability of failure on a single trial.
- n is the total number of trials.
- k is the number of successes we are interested in.
- In this case, we are interested in the probability of making the fifth shot on the eighth attempt (k = 1) and the total number of attempts is 8 (n = 8). The probability of making a free throw (success) is 80% or 0.8 (p = 0.8).
Let's calculate the probability:
P(X = 1) = C(8, 1) * 0.8^1 * (1 - 0.8)^(8 - 1)
C(8, 1) = 8! / (1! * (8 - 1)!) = 8
P(X = 1) = 8 * 0.8 * 0.2^7 ≈ 0.2013
So, the probability that Joe Biden makes his fifth shot on his eighth attempt is approximately 0.2013 or 20.13%.