Question

A chromosome mutation believed to be linked with colorblindness is known to occur, on the average, once in every 10,000 births. If 20,000 babies are born this year in a certain city:

1. What is the probability that at least one will develop colorblindness?
2. What is the exact probability model that applies here?
3. Approximate the probability that 2 or more babies will develop colorblindness, using the appropriate Poisson model.

Answer 1

0.8647,0.5940

Explanation:

Given that a chromosome mutation believed to be linked with colorblindness is known to occur, on the average, once in every 10,000 births.

Hence for a sample of 20000 babies we can take average as 2.

2) Since n is very large and p is small but np is finite Poisson model applies here.

1) the probability that at least one will develop colorblindness

=
`P(X\geq 1) = 0.86466`

3) the probability that 2 or more babies will develop colorblindness, using the appropriate Poisson model.

=
`P(x\geq 2) = 0.59399`