A certain rare blood type can be found in only 0.05% of people. If the population...

A certain rare blood type can be found in only 0.05% of people. If the population of a randomly selected group is 3000, Find the probability that

two persons in the group have this rare blood type.

1 person in the group has this rare blood type.

at least two persons in the group have this rare blood type.

Solutions

Expert Solution

The total number of persons in a group (n) is 3000.

The probability of having a certain rare blood type (p) is 0.05% or 0.0005.

Let X denotes the number of persons with rare blood type. So, X follows binomial(3000, 0.0005).

The pmf of binomial distribution is,

(a). The probability that two persons in the group have this rare blood type is given by,

Therefore, the probability that two persons in the group have this rare blood type is 0.2511.

(b).

The probability that 1 person in the group have this rare blood type is given by,

Therefore, the probability that 1 person in the group have this rare blood type is 0.3347.

(c). The probability that at least two persons in the group have this rare blood type is given by,

Therefore, the probability that at least two persons in the group have this rare blood type is 0.4423.

orchestra answered 1 year ago

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