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

• A. The probability that A wins and loses equal number of matches is $\frac{34}{81}$
• B. The probability that A wins and loses equal number of matches is $\frac{17}{81}$
• C. The probability that A wins more number of matches than it loses is $\frac{17}{81}$
• D. The probability that A loses more number of matches than it wins is $\frac{16}{81}$

Answer 1

The correct option is B The probability that A wins and loses equal number of matches is $\frac{17}{81}$

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
$={\left(\frac{1}{3}\right)}^5{+}^5{C}_1{.}^4{C}_1{\left(\frac{1}{3}\right)}^5{+}^5{C}_2{.}^3{C}_2{\left(\frac{1}{3}\right)}^5=\frac{17}{81}$