if on an average vessel in every 10 wrecked.find the probability that out of 5 vessels expected to arrive at least 4 will arrive safetly?
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How many vessels in every 10 are wrecked ?
0.0017
To find the probability that out of 5 vessels expected to arrive, at least 4 will arrive safely, we need to use the concept of the binomial distribution.
In this case, we have a success (a vessel arriving safely) and a failure (a vessel getting wrecked). The probability of success is denoted by p, and in this case, p = 1/10 (since, on average, one out of every 10 vessels is wrecked).
The probability of failure (getting wrecked) is denoted by q, and q = 1 - p = 1 - 1/10 = 9/10.
We want to find the probability of at least 4 vessels arriving safely out of the 5 vessels expected to arrive, which means we need to find the probability of 4 safe vessels and the probability of 5 safe vessels.
The probability of getting exactly k successes out of n trials, where each trial has a probability p of success, can be calculated using the binomial probability formula:
P(X = k) = (n C k) * p^k * q^(n - k)
Where (n C k) represents the combination function and equals n! / (k!(n - k)!)
To find the probability of at least 4 vessels arriving safely, we sum up the probabilities of having exactly 4 and 5 safe vessels:
P(X >= 4) = P(X = 4) + P(X = 5)
P(X = 4) = (5 C 4) * (1/10)^4 * (9/10)^(5 - 4)
= 5 * (1/10000) * (9/10)
= 45/100000
P(X = 5) = (5 C 5) * (1/10)^5 * (9/10)^(5 - 5)
= 1 * (1/100000) * 1
= 1/100000
P(X >= 4) = 45/100000 + 1/100000
= 46/100000
Therefore, the probability that out of 5 vessels expected to arrive, at least 4 will arrive safely is 46/100000.