If on an average, one ship out of 10 is wrecked. Find the probability that out of five ships expected to arrive the post at least four wil arrive safely.
To find the probability that at least four out of five ships will arrive safely, we need to consider the possible combinations of ship arrivals.
Let's start by finding the probability of exactly four ships arriving safely and one ship being wrecked.
The probability that a ship arrives safely is 9/10, and the probability that a ship is wrecked is 1/10.
So, for exactly four ships to arrive safely and one ship to be wrecked, we have:
Probability = (9/10) * (9/10) * (9/10) * (9/10) * (1/10) = (9/10)^4 * (1/10) = (6561/10000) * (1/10) = 6561/100000.
Next, we consider the probability that all five ships arrive safely.
For all five ships to arrive safely, the probability is:
Probability = (9/10)^5 = 59049/100000.
Now, we add the probabilities of exactly four ships arriving safely and all five ships arriving safely:
Total probability = (6561/100000) + (59049/100000) = 6561/100000 + 59049/100000 = 6561 + 59049/100000 = 65610/100000 = 0.6561.
Therefore, the probability that at least four out of the five ships will arrive safely is 0.6561, or 65.61%.