Only about 80% of all donated human blood can be used in hospitals. The remainin

Question

Only about 80% of all donated human blood can be used in hospitals. The remaining 20% cannot be used because of various infections in the blood. Suppose a blood bank has 10 newly donated pints of blood. Let r be a binomial random variable that represents the number of "good" pints that can be used.

(a) Based on questionnaires completed by the donors, it is believed that at least 6 of the 10 pints are usable. What is the probability that at least 8 of the pints are usable, given this belief is true? Compute P(8 r | 6 r). (Round your answer to three decimal places.)

(b) Assuming the belief that at least 6 of the pints are usable is true, what is the probability that all 10 pints can be used? Compute P(r = 10 | 6 r). (Round your answer to three decimal places.)

Explanation / Answer

probability that blood can be used = 0.8

probability that blood canot be used = 0.2

a) FOR r>=6 = p(6)+p(7)+p(8)+p(9)+p(10)

p(6)= 10C6*(0.8)^6*(0.2)^4 = 0.015

P(7) = 10C7*(0.8)^7*(0.2)^3 = 0.201

P(8) = 10C8*(0.8)^8*(0.2)^2 = 0.301

P(9) = 10C9*(0.8)^9*(0.2) = 0.268

P(10)= 0.8^10 = 0.107

ADDING ALL WE GET = 0.892

A)P(8<=r/6<=r)= 0.676/0.892 = 0.757

b)p(r=10/6<=r) = 0.107/0.892 = 0.119

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