A school nurse knos from past experience that 60 percent of the children who vis

Question

A school nurse knos from past experience that 60 percent of the children who visit him will have either flu or chicken pox (or possibly both). He also knows that 18 percent of the children who visit him will have chicken pox but not the flu, and 40 percent of the children who visit him will have flu or not chicken pox.

A) Calculate the probability that a child who visits the nurse wil have neither flu nor chicken pox. (That is, not have chicken pox and also not the flu)

B) Calculate the probability that a child who visits this nurse will have both flu and also chicken pox

Explanation / Answer

I'm assuming that the 'or' in and "40 percent of the children who visit him will have flu or not chicken pox." is supposed to be an 'and'. Otherwise the sentence doesn't make sense. A) 60% of children have either chicken pox or the flu. --> 40% of children have neither. B) 18% have chicken pox but no flu. 40% have the flu but no chicken pox. --> 2% of children have chicken pox and the flu. If you want a more formal way of doing it: A={chicken pox} B={flu} P(A u B)=0.6 P(A but no B)=0.18 P(B but no A)=0.4 P(A u B)=P(A but no B)+P(B but no A)+P(A n B) --> 0.6=0.18+0.4+X --> 0.6-0.18-0.4=0.02=X

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