Only 4% of people have Type AB blood. A hospital blood bank needs Type AB blood
ID: 3177860 • Letter: O
Question
Only 4% of people have Type AB blood. A hospital blood bank needs Type AB blood so the blood bank begins checking potential donors.
Use this Excel file geometric probabilities (enable the macro after opening the file) or this Excel file geometric probabilities 2 to assist you with the geometric probability calculations required to answer the questions below.
What is the probability that the first Type AB donor is the fourth person checked?
On average, how many donors must be checked until the first donor with Type AB blood is found?
What is the probability that there is a Type AB donor among the first 5 donors checked?
What is the probability that we won't find a Type AB donor before the tenth person, that is, what is the probability that the first Type AB donor is not among the first 9 donors?
Explanation / Answer
probability that the first Type AB donor is the fourth person checked=P(first 3 are other blood group*4th has AB blood group) =(1-0.04)3*0.04 =0.0354
number of donors required =1/p=1/0.04=25
probability that there is a Type AB donor among the first 5 donors checked =1-P(no AB blood group among first 5)
=1-(1-0.04)5 =0.1846
probability that the first Type AB donor is not among the first 9 donors =(1-0.04)9 =0.6925
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