Multiple choice

$A$ and $B$ play a match in which the chances of their winning a game is $\frac{1}{4}$ for both of them and $\frac{1}{2}$ is the probability that match is being drawn. Match is finished as soon as either player wins two games. Find the probability that the match will be finished in $4$ or less games.

  1. $\dfrac{9}{16}$
  2. $\dfrac{7}{16}$
  3. $\dfrac{1}{2}$
  4. $\dfrac{1}{4}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P(A wins) = 1/4, P(B wins) = 1/4, P(Draw) = 1/2. Match ends when someone wins 2 games. Possible sequences for 2, 3, or 4 games: (AA), (BB), (A, not A, A), (B, not B, B), etc. This is a standard probability problem. The probability of finishing in 4 or less games is 1/2.

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