Final answer:
To calculate the probability that at least 5 vessels transporting nuclear weapons were destroyed, we can use the concept of combinations. By finding the probability of exactly 5 vessels being destroyed and the probability of all 6 vessels being destroyed, we can add these probabilities together to get the final answer.
Step-by-step explanation:
To solve this problem, we can use the concept of combinations. The probability can be calculated by finding the probability that exactly 5 vessels transporting nuclear weapons were destroyed, and then adding the probability that all 6 vessels transporting nuclear weapons were destroyed.
To find the probability that exactly 5 vessels transporting nuclear weapons were destroyed, we can use the formula:
P(5 vessels destroyed) = C(8,5) × C(9,1) / C(17,6) = 56/816
To find the probability that all 6 vessels transporting nuclear weapons were destroyed, we can use the formula:
P(6 vessels destroyed) = C(8,6) × C(9,0) / C(17,6) = 28/816
To find the probability that at least 5 vessels transporting nuclear weapons were destroyed, we can add the two probabilities:
P(at least 5 vessels destroyed) = P(5 vessels destroyed) + P(6 vessels destroyed) = (56+28)/816 = 84/816 = 0.1029 (rounded to four decimal places).