Brazilian scientists have identified an new strain of the H1N1 virus. The geneti

Question

Brazilian scientists have identified an new strain of the H1N1 virus. The genetic sequence of the new strain consists of alterations in the hemagglutin protein, making it significantly different from the usual H1N1 strain. Public health officials wish to study the population of residents in Rio de Janeiro. Suppose that in this population the probability of catching the usual strain is .10, the probability of catching the new strain is .05, and the probability of catching both strains is .01. a. In this setting, are the events "catching the usual strain" and "catching the new strain" mutually exclusive? Why? b. What is the probability of not catching the new strain? c. What is the probability of catching exactly one type of strain? d. What is the probability of catching the usual type but not the old type? e. What is the probability of catching at least one of the two strains? f. What is the probability of not catching neither one of the two strains?

Explanation / Answer

From the given information we have

P(catching usual strain) = 0.10,P(catching new strain) = 0.05, P(catching both strain) = 0.01

(e)

By the addition rule of probability, the probability of catching at least one of the two strain is

P(catching at least one strain)= P(catching usual strain)+P(catching new strain) - P(catching both strain) = 0.10 +0.05 - 0.01 = 0.14

(f)

By the complement rule, the probability of not catching neither one of the two strains is

P(catching no strain) =1 - P(catching at least one strain)=1 - 0.14 = 0.86

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