I virus. The genetic sequence of the new strain consists of alterations in the h

Question

I virus. The genetic sequence of the new strain consists of alterations in the hemagglutin protein, making it significantly different from the usual HINI 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 sual 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

a) as probability of catching the new strain and usual strain is 0.01 and not equal to 0 . They are not mutually exclusive/

b) P(not catching new strain) =1-P(catching new strain) =1-0.05 =0.95

c) P(exactly one type)=P(catching new strain)+P(catching usual strain)-2*P(catching both type)

=0.05+0.1-2*0.01=0.13

d) P(catching usual but not old) =P(catching usual)-P(catching both type) =0.1-0.01=0.09

e)P(catching at least one )=P(catching new strain)+P(catching usual strain)-P(catching both type)

=0.05+0.1-0.01=0.14

f) P(not catching neither )=1-P(catching at least one ) =1-0.14 =0.86

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