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Answer :
Final answer:
The question is about calculating the cumulative binomial probability that Pete will catch fish on one day or less given the probability of Pete catching fish per day is 0.20. The probabilities for individual outcomes can be calculated using the binomial formula, and summed to get the required probability.
Explanation:
In this problem, we have a random variable X which represents the number of days Pete catches fish in a week. As Pete is fishing for 3 days, the possible values for X can be 0, 1, 2, or 3. The probability of Pete catching fish is 0.20, and it remains the same for each day he goes fishing.
To find the probability that Pete will catch fish on one day or less (P(X ≤ 1)), we need to add up the probabilities of catching fish on 0 days (P(X=0)) and 1 day (P(X=1)). These probabilities can be calculated using the binomial probability formula, which is P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)) where n is the number of trials (3 days), k is the number success (0 or 1 day), p is the probability of success (0.20) and C(n, k) is the binomial coefficient that tells the number of ways to choose k successes from n trials.
Computations using these formulas will yield the probabilities for each possible outcome, adding them will provide the probability that Pete will catch fish on one day or less. Unfortunately, the question seems to lack a specific numerical value for the asked probability.
Learn more about Binomial Probability here:
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