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Answer :
Final answer:
The probability that Pete will catch fish on one day or less over three days, with each day having a probability of 0.84 of catching a fish, is approximately 0.065. This is calculated using the binomial distribution formula.
Explanation:
The subject of this question is the concept of probability in mathematics. To answer the question, we need to calculate the probability that Pete will catch fish on one day or less in a three-day period where each day he has the probability of 0.84 of catching a fish.
When Pete goes fishing, he either catches fish (which we can denote as 'success') or he doesn't (which we can denote as 'failure'). The probability of success p is 0.84, meaning the probability of failure q is 1 - p = 0.16.
Now we need to calculate the probability that Pete catches fish on exactly 0 days (which equates to 3 failures) or exactly 1 day (which equates to 2 failures and 1 success), as described by the binomial distribution formula:
P(X = k) = nCk * (p^k) * (q^(n-k))
where P is the probability, n is the number of trials, k is the number of successes, and nCk is the combinations of n choose k.
So the probability that Pete catches fish on 0 day is:
P(X = 0) = 3C0 * (0.84^0) * (0.16^3)≈ 0.004
And the probability that Pete catches fish on 1 day is:
P(X = 1) = 3C1 * (0.84^1) * (0.16^2)≈ 0.061
The probability that Pete catches fish on one day or less is, therefore, the sum of these two probabilities, which is approximately 0.065. The correct answer is option a) 0.065.
Learn more about Probability here:
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