Doctors have found that in many tropical regions, people who are carriers of the

Question

Doctors have found that in many tropical regions, people who are carriers of the sickle-cell gene are more resistant to malaria. Suppose that in a specific community, 8% of the population carries the sickle-cell gene. The probability of dying of malaria for people in this community without the sickle-cell gene is 20%, while those who do carry the gene die from malaria with a probability of only 7%.

a. Suppose someone in this community is infected with malaria. What is the probability
that this person is a carrier of the sickle-cell gene and survives?

b. What is the probability that in a group of 3 random individuals in this community, none
are carriers of the sickle-cell gene?

c. Are dying from malaria and being a carrier of the sickle-cell gene independent events?
Explain your answer.

Explanation / Answer

a.

P(sickle cell gene and survives) = 0.08*(1-0.07) = 0.0776

b.

P(none of 3 random individuals are carrier of sickle cell gene)= 0.92*0.92*0.92 = 0.778688

We are multiplying the probabilities here because the probability of each individual being a carrier of sickle cell gene is independent of each other. And in case of 3 independent events happening together their combined probability is a obtained by multiplying probability of each independent event.

c.

No they are not independent events.

P(Sickle cell gene|dying) = 0.08*0.07/(0.08*0.07+0.92*0.20)= 0.03 . This is not equal to the probability of P(sickle gene cell) . If these events were independent these two probabilities would be equal.

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