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Answer :
The probability that exactly 5 of Pete's friends will pass the CPA exam is approximately 0.275
This problem can be solved using the binomial distribution. We know that the probability of passing the CPA exam for a graduate of Pete's College of Business is p = 0.71.
We also know that there are eight friends taking the exam, so the number of trials (n) is 8. We want to find the probability that exactly 5 of them will pass.
The formula for the probability mass function of the binomial distribution is
P(X = k) = (n choose k) × p^k × (1-p)^(n-k)
where X is the random variable representing the number of successes (i.e., the number of Pete's friends who pass), k is the number of successes we want to find (i.e., 5), (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials, and p is the probability of success (i.e., 0.71).
Plugging in the numbers, we get
P(X = 5) = (8 choose 5) × 0.71⁵ × (1-0.71)³
= 56 × 0.71 × 0.29³
≈ 0.275
Learn more about probability here
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