Assume that on an average one telephone number out of 15 , called between 3 p.m. and 4 p.m on weekdays will be busy . What is the probability that if six randomly selected telephone numbers are called at least 3 of them will be busy?

Answer

`1-((14)/(15))^(4).((59)/(45))`

Explanation

`p=(1)/(15),q=(1-(1)/(15))=(14)/(15) " and " n=6`
`P(X =r) =.^(n)C_(r ).p^( r).q^((n-r)) =.^(6)C_(r ) .((1)/(15))^(r ).((14)/(15))^((6-r))`
`P(X ge 3) =1- P(X lt3) =1- [P(X=0) +P(X=1)+P(X=2)]`
`=1-[.^(6)C_(0) .((14)/(15))^(6) +.^(6)C_(r ) .((1)/(15)).((14)/(15))^(5)+.^(6)C_(2).((1)/(15))^(2).((14)/(15))^(4)]`
`=1-((14)/(15))^(4).((59)/(45))`