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Answer :
Final answer:
The random variable X is defined as the number of days Pete catches fish. The probability that Pete will catch fish on exactly one day is 0.096.
Explanation:
The random variable X is defined as the number of days Pete catches fish when he goes fishing.
To find the probability that Pete will catch fish on exactly one day, we can use the binomial probability formula. The formula is:
P(x) = (n C x) * p^x * (1-p)^(n-x)
where n is the number of trials (in this case, 3 days), x is the number of successes (in this case, 1 day), and p is the probability of success (in this case, 0.8).
Plugging in the values, we get:
P(x = 1) = (3 C 1) * 0.8^1 * (1-0.8)^(3-1) = 3 * 0.8 * 0.2^2 = 0.096
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