In kidney transplantations, compatibility between donor and receiver depends on such factors as blood type and antigens. Suppose that for a randomly selected donor from a large national kidney registry, there is a 10% chance that he or she is compatible with a specific receiver. A sample of size 5 donors are randomly selected from this registry. Find the probability that exactly 2 of the selected donors is compatible.

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okpalawalter8 okpalawalter8 · Answer 1 · 2020-10-21T18:05:08+02:00

Answer:

The probability is [tex]P(X = 2)= 0.0729[/tex]

Step-by-step explanation:

From the question we are told that

The percentage that the donor is compactible is p = 0.10

The sample size is n = 5

Generally the probability that the donor is not compactible is

[tex]q = 1- p[/tex]

=> [tex]q = 1- 0.10 [/tex]

=> [tex]q = 0.90 [/tex]

Generally the probability that the exactly 2 of the selected donors is compatible mathematically represented as

[tex]P(X = 2)= \ ^{5}C_2 * p^2 * q^{5-2}[/tex]

Here C standards for combination

=> [tex]P(X = 2)= \ 10 * 0.10^2 * 0.90 ^{5-2}[/tex]

=> [tex]P(X = 2)= 0.0729[/tex]