A football match may be either won, drawn or lost by the host country's team. So there are threeways of forecasting the result of any one match, one correct and two incorrect. Find the probability of forecasting at least three correct results for four matches.

Options

A. `(1)/(9)`
B. `(2)/(9)`
C. `(2)/(7)`
D. None

Answer

A

Explanation

p=P (correct forecasting) = `(1)/(3)`
q=P (wrong forecasting)= `(2)/(3)`
n=4
let r be the number of correct forecast
P(At least three correct results). ltb rgt = P(r=3)+P(r=4)
`P=""^(4)C_(3)(p)^(3)(q)^(1)+""^(4)C_(4)(p)^(4)(q)^(0)`
`P=4((1)/(3))^(3)((2)/(3))+((1)/(3))^(4) `
= `((1)/(3))^(3)((8)/(3)+(1)/(3))`
`3xx(1)/(27)=(1)/(9)`