To calculate the probability that at least 4 out of 6 fish weigh more than 1.4 kg, we need to consider the different combinations of fish that satisfy this condition.
Let's calculate the probabilities of the different scenarios:
1. All 6 fish weigh more than 1.4 kg: The probability of a fish weighing more than 1.4 kg is denoted as p. Since all 6 fish need to meet this condition, the probability is p^6.
2. Exactly 5 fish weigh more than 1.4 kg: We need to choose 5 out of the 6 fish that meet the condition, and the remaining 1 fish should weigh 1.4 kg or less. The probability is calculated as (6 choose 5) * p^5 * (1-p)^1.
3. Exactly 4 fish weigh more than 1.4 kg: We need to choose 4 out of the 6 fish that meet the condition, and the remaining 2 fish should weigh 1.4 kg or less. The probability is calculated as (6 choose 4) * p^4 * (1-p)^2.
To calculate the probability of at least 4 fish weighing more than 1.4 kg, we sum up the probabilities of the above three scenarios:
Probability = p^6 + (6 choose 5) * p^5 * (1-p)^1 + (6 choose 4) * p^4 * (1-p)^2.
Please note that the exact value of p (probability of a fish weighing more than 1.4 kg) is not provided in the question, so we would need that information to calculate the numerical probability.