Final answer:
To determine the probability of catching a certain number of fish based on a given success rate, we use the binomial distribution. The probabilities for catching 12 or fewer, 5 or more, and between 5 and 12 fish out of 24 strikes are calculated using the binomial probability formula.
Step-by-step explanation:
The question involves calculating probabilities for a specific number of successful events (catching fish) given a total number of trials (strikes) based on a known probability for success. Since each strike can be seen as a Bernoulli trial with two possible outcomes (catch or no catch), with a fixed success probability of 44%, we can model this scenario with a binomial distribution where the number of trials, n, is 24, and the success probability, p, is 0.44.
Calculating the Probabilities
To solve the mathematical problem completely, we use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where 'k' is the number of successful catches. We want to find the probabilities for the following scenarios:
- (a) 12 or fewer catches: We need to sum the probabilities for k=0 to k=12.
- (b) 5 or more catches: Since it is more efficient to calculate the complement, we find the sum of probabilities for k=0 to k=4 and subtract from 1.
- (c) Between 5 and 12 catches: We calculate the sum of probabilities for k=5 to k=12.
Calculations would typically be done with a binomial calculator or using statistical software, as manual calculation can be cumbersome. The resulting probabilities provide an understanding of the likely outcomes based on given strike success rates.