A certain team wins with probability 0.7, loses with probability 0.2and ties with probability .1 the team plays three games. Find the probability that the team wins at least two of the games, but not lose.

Explanation

Let A, B and C denote the events that the teamAins, loses and ties respectively.
therefore {P}({A})=0.7, {P}({B})=0.2, {P}({C})=0.1

`therefore`Required probability ={P} (teamAins at least two games but not loses) =P(AA C)+P(A CA)+P(CAA)+P(AAA)

`=P(A) P(A) P(C)+P(A) P(C) P(A)+P(C) P(A) P(A)+P(A) P(A) P(A)`

`=3[P(A) P(A) P(C)]+P(A) P(A) P(A)`

`=3[(0.7)(0.7)(0.1)+(0.7)(0.7)(0.7)`

`=3 times 0.049+0.343=0.147+0.343`

`=0.49`