People with type O-negative blood are universal donors whose blood can be safely given to anyone. Only 8% of the population have O-negative blood. A blood center is visited by 5 donors in an afternoon. What is the probability that there are no universal donors among them? Round your answer to four decimal places.

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MrRoyal MrRoyal · Answer 1 · 2020-11-02T16:04:36+01:00

Answer:

[tex]Probability = 0.6591[/tex]

Step-by-step explanation:

Given

Represent P(O-Negative) with p

So:

[tex]p = 8\%[/tex]

Convert to decimal

[tex]p = 0.08[/tex]

Required

Determine the probability that none out of 5 is O-Negative

First, we need to determine the probability that one person is not O-Negative

Represent this with q

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

[tex]q = 1 - 0.08[/tex]

[tex]q = 0.92[/tex]

To determine the probability that none out of five, we have:

[tex]Probability = q^n[/tex]

Where

[tex]n = 5[/tex]

So, we have:

[tex]Probability = 0.92^5[/tex]

[tex]Probability = 0.6590815232[/tex]

[tex]Probability = 0.6591[/tex] --- Approximated