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.
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
Thank you very much.. :)
To find the probability that Team B will score 5 points in the series, we need to consider all the possible outcomes.
There are three possible outcomes in each match: win, loss, or draw. Since there are 5 matches in the series, there are a total of 3^5 = 243 possible outcomes.
Now, let's determine the number of outcomes where Team B scores 5 points. To score 5 points in the series, Team B must win all 5 matches. Since the probability of B winning a match is 1/3, the probability of B winning all 5 matches is (1/3)^5 = 1/243.
Therefore, the probability that B will score 5 points in the series is 1/243.