SOLUTION: in a long run 3 ships out of every 100 are sunk if 10 ship are out what is the probability that all will arrive safely

Question 1024654: in a long run 3 ships out of every 100 are sunk if 10 ship are out what is the probability that all will arrive safely
Found 2 solutions by FrankM, mathmate:
Answer by FrankM(1040) (Show Source): You can put this solution on YOUR website!
each ship has 97% chance of survival.
.97^10 = .7374 or 73.74% chance of all 10.
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
in a long run 3 ships out of every 100 are sunk if 10 ship are out what is the probability that all will arrive safely.

Solution:
The binomial distribution seems an appropriate model. In order to model using binomial, we need to make the following assumptions:
1. the probability of sinking (3/100=0.03) remains constant
2. all 10 ships in the experiment (model) are random and independent.

The binomial distribution with n=10 steps, and probability p=0.03 of "success" is given by
P(x;n;p)=
where
x is the number of successes (ship sinking) (0)
n size of fleet (10)
p probability of success, (sinking) (0.03)
C(n,x)=n!/(x!(n-x)!) is the binomial coefficient.

Using x=0, n=10, p=0.03
P(0,10,0.03)
=
=0.7374
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