Team A plays with 5 other teams exactly once. Assuming that for each match the probabilities of a win, draw and loss are equal, then Options: A . &nbspThe probability that A wins and loses equal number of matches is 3481 B . &nbspThe probability that A wins and loses equal number of matches is 1781 C . &nbspThe probability that A wins more number of matches than it loses is 1781 D . &nbspThe probability that A loses more number of matches than it wins is 1681

Team A plays with 5 other teams exactly once. Assuming that for each match the p

Question

Team A plays with 5 other teams exactly once. Assuming that for each match the probabilities of a win, draw and loss are equal, then

Options:

A . The probability that A wins and loses equal number of matches is 3481

B . The probability that A wins and loses equal number of matches is 1781

C . The probability that A wins more number of matches than it loses is 1781

D . The probability that A loses more number of matches than it wins is 1681

Answer: Option B
:
B
Probability of equal number of W and L is the probability of following
(0)W,(0)L +(1)W,(1)L+(2)W, (2)L

= {(\frac{1}{3})}^{5} +^{5} C_{1} .^{4} C_{1} {(\frac{1}{3})}^{5} +^{5} C_{2} .^{3} C_{2} {(\frac{1}{3})}^{5} = \frac{17}{81}

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