Question

Suppose 20 donors come to a blood drive. Assume that the blood donors are not related in any way, so that we can consider them to be independent. The probability that a donor has type "O" blood is 0.06. What is the probability that 1 or more donors have type O blood? A. 0.370 B. 0.290 C. 0.630 D. 0.710

Answer 1

Given Information:

Probability of success = p = 0.06

Number of trials = n = 20

Required Information:

Probability of 1 or more donors of "O" blood group = ?

Answer:

P( x ≥ 1 ) = 0.710

Explanation:

We are given the probability that a donor has type "O" blood group.

We want to find out the probability of having 1 or more donors who has type "O" blood group out of 20 donors.

P( x ≥ 1 ) = 1 - P( x = 0)

So we will first find the probability that none of the donors has type "O" blood group then we will subtract that from 1 to get the probability of having 1 or more donors with "O" blood group.

P( x = 0) = (p⁰)(1 - p)²⁰

P( x = 0) = (0.06⁰)(1 - 0.06)²⁰

P( x = 0) = (1)(0.94)²⁰

P( x = 0) = 0.290

So the probability of having 1 or more donors with "O" blood group is

P( x ≥ 1 ) = 1 - P( x = 0)

P( x ≥ 1 ) = 1 - 0.290

P( x ≥ 1 ) = 0.710

P( x ≥ 1 ) = 71%

Therefore, the correct answer is D. 0.710