Question

in a series of 5 one day cricket matches between A and B, the probability of B winning or making draw are 1/3 & 1/6 respectively. If a win, loss or draw gives 2,0 or 1 points respectively, find the probability that B will score 5 points in the series.

Answer 1

Assuming they play all 5 games,
to get 5 points in 5 matches, it could be

DDDDD --- arranged in 1 way
WDDDL --- arranged in 5!/3! or 20 ways
WWDLL--- arranged in 5!/(2!2!) or 30 ways

Prob(win) = 1/3
prob(draw) = 1/6
prob(loss) = 1/2

prob(DDDDD) = (1/6)^5 = 1/7776
prob(WDDDL) = 20(1/3)((1/6)^3(1/2) = 5/324
prob(WWDLL) = 30(1/3)^2 (1/6)(1/2)^2 = 5/36

prob(scoring 5 points) = 1/7776 + 5/324+5/36
= 1201/7776 = appr .1544

Answer 2

Thank you very much.. :)