Question

The probability that a salmon swims successfully through a dam is 0.59 Find the probability that out of 3 salmon at least one is successful?

Answer 1

Solution:
P(Salmon Swims Successfully through a dam) = 0.59
Number of sample = 3
We need to calculate the probability that out of 3 salmon at least one is successful i.e. P(X>=1) =?

Here we will use binomial distribution probability as all events are independent events which can be calculated as
P(X=n |N,p) = NCn*(p^n)*(1-p)^(N-n)
P(X>=1) = P(X=1) + P(X=2) + P(X=3) = 3C1*(0.59^1)*(1-0.59)^(3-1) + 3C2*(0.59^2)*(1-0.59)^(3-2) + 3C3*(0.59^3)*(1-0.59)^(3-3) = 3*0.59*0.1681 + 3*0.3481*0.41 + 1*0.2054 = 0.2975 + 0.4282 + 0.2054 = 0.9311
So there is 93.11% probability that out of 3 salmon at least one is successful.