Problem 3. Probability. (10 pts) A bin contains three types of influenza A vacci

Question

Problem 3. Probability. (10 pts) A bin contains three types of influenza A vaccines: HN1, H3N2 and H10N7. The probability that the HIN1 vaccine will last one season is 0.4, with the corresponding probabilities of the H3N2 and H10N7 vaccines being 0.5 and 0.1, respectively. Suppose that 30% of the vaccines in the bin are for H1N1, 50% for H3N2 and 20% fir H10N7. a) What is the probability that a vaccine chosen at random will last one season? b) Given that a vaccine lasted an entire season, what is the conditional probability that it was for H10N7

Explanation / Answer

Ans:

Given that

P(last one season/HINI)=0.4

P(last one season/H3N2)=0.5

P(last one season/H10N7)=0.1

P(H1N1)=0.30

P(H3N2)=0.50

P(H10N7)=0.20

a)P(last one season)=P(last one season/HINI)*P(H1NI)+P(last one season/H3N2)*P(H3N2)+P(last one season/HI0N7)*P(H10N7)

=0.4*0.3+0.5*0.5+0.1*0.2=0.39

b)P(H10N7/last one season)=0.1*0.2/0.39=0.0513

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