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Answer :
The probability that Pete will catch fish on a particular day when he goes fishing is .8. Peter is going fishing for 3 days. The variance of the number of days Pete will catch fish is 0.48. Therefore, option a) is correct.
To determine the variance of the number of days Pete will catch fish, we need to consider that the probability of catching fish on any given day is 0.8. Let's denote a successful day of catching fish as "1" and an unsuccessful day as "0."
We can model Pete's fishing days as a binomial distribution, where the probability of success (catching fish) is p = 0.8, and the number of trials is n = 3. The variance of a binomial distribution is given by the formula: Var(X) = np(1-p).
Using this formula, we can calculate the variance:
Var(X) = 3 * 0.8 * (1 - 0.8)
= 3 * 0.8 * 0.2
= 0.48
Therefore, the variance of the number of days Pete will catch fish over the three-day fishing trip is 0.48.
In conclusion, the correct answer is option a) 0.48. This variance indicates the spread or variability in the number of days Pete is expected to catch fish, based on the given probability of 0.8.
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Complete Question:
The probability that Pete will catch fish on a particular day when he goes fishing is .8. Peter is going fishing for 3 days. The variance of the number of days Pete will catch fish is?
a) 0.48
b) .8
c) 2.4
d) 0.16
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