Question

Once a sea turtle hatching makes it from the beach to the sea, its probability of surviving to adulthood is 3/5. In a group of four hatchings that have made it to the sea, what is the probability that two will survive to adulthood? What is the probability that at least one will survive to adulthood?

Answer 1

a)

Here, n = 4, p = 0.6, (1 - p) = 0.4 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 2)
P(X = 2) = 4C2 * 0.6^2 * 0.4^2
P(X = 2) = 0.3456
0

b)

Here, n = 4, p = 0.6, (1 - p) = 0.4 and x = 1
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 1).
P(X >= 1) = (4C1 * 0.6^1 * 0.4^3) + (4C2 * 0.6^2 * 0.4^2) + (4C3 * 0.6^3 * 0.4^1) + (4C4 * 0.6^4 * 0.4^0)
P(X >= 1) = 0.1536 + 0.3456 + 0.3456 + 0.1296
P(X >= 1) = 0.9744