Answer to Question #343200 in Statistics and Probability for Olic5. The probab

Question

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

Answer 1

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

Given $n=7, q=2/5=0.4, p=1-q=0.6.$

(i)

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

(ii)

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