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Answer :
The correct answer is a probability of 0.104.
To solve the problem, we need to define the random variable X as the number of days Pete catches fish when he goes fishing for 3 days. The probability that Pete catches fish on any given day is 0.8, so we can state this as
P(X = 1) = 0.8 for catching fish on a single day.
However, we want to find the probability of Pete catching fish on one day or less, which can be represented as
P(X \<= 1). This includes the scenarios where Pete catches fish on zero days (P(X = 0)) or on one day (P(X = 1)).
To find these probabilities, we need to consider the complementary probabilities and use the binomial formula.
P(X = 0) would be calculated as (1 - 0.8)³, which is the probability Pete doesn't catch fish on any of the three days.
P(X = 1) would be 3 × 0.8 × (1 - 0.8)², which is the probability Pete catches fish on exactly one day out of three, considering the different permutations of when he could catch fish.
After calculating these two probabilities, we add them together to find P(X \<= 1).
Therefore, the correct answer is (1 - 0.8)³ + 3 × 0.8 × (1 - 0.8)² = 0.008 + 0.096 = 0.104. So, the correct answer to the question is d. 0.104.
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Answer:
So the correct option for this case would be:
0.48
