Question #343200

5. The probability that a woman does not know swimming is 2/5. If seven women in a city are 

selected at random, find probability that

(i) four women know swimming.

(ii) at least one woman knows swimming


1
Expert's answer
2022-05-23T23:40:55-0400

 Let X=X= the number of female who knows swimming : XBin(n,p).X\sim Bin (n, p).

Given n=7,q=2/5=0.4,p=1q=0.6.n=7, q=2/5=0.4, p=1-q=0.6.

(i)


P(X=4)=(74)(0.6)4(0.4)74=0.290304P(X=4)=\dbinom{7}{4}(0.6)^4(0.4)^{7-4}=0.290304



(ii)


P(X1)=1P(X=0)P(X\ge 1)=1-P(X=0)=1(70)(0.6)0(0.4)70=0.9983616=1-\dbinom{7}{0}(0.6)^0(0.4)^{7-0}=0.9983616


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