Hello, KelvinScale!

In a large population, people are one of three genetic types: A, B, C:

. . 30% are Type A, 60% are Type B, and 10% are Type C.

The probability a person carries certain gene making them susceptible for a disease

. . is 0.05 for A, 0.04 for B, and 0.02 for C.

If ten people are selected randomly, what is the probability at least one has that gene?

30% of the population are Type A; 5% of them have the gene.

. . We have: .

1.5% of the population are Type A and have the gene.

60% of the population are Type B; 4% of them have the gene.

. . We have: .

2.4% of the population are Type B and have the gene.

10% of the population are type C; 2% of them have the gene.

. . We have: .

0.2% of population are Type C and have the gene.

Hence: . of the population has the gene.

. . and: . do not have the gene.

Ten people are selected at random.

We want probability thatat least oneof them has the gene.

The opposite of "at least one has the gene" is "none of them has the gene".

We know that:.

Therefore: .