The probability that the first game is a draw is the probability thatOriginally Posted by Kiwigirl
neither wins, and since A wins with probability 0,4 and B wins with
probability 0.5, the probability of a draw on any game is 1-0.4-0.5=0.1.
Therefore the probability that the first game is a draw is the probability
that any game is a draw and is equal to 0.1
[The results of each of the first three games are independent, and theb) the probability A wins the first three games
probability of A winning in any one of them is 0.4 so the probability of
A winning the first three games is the product of the probabilities of
A winning each of them=0.4x0.4x0.4=0.064
There are two ways that the tournament can be just three games long;c) the probability the tournament is just three games long
A can win the first three games, or B can win the first three games. The
probabilities of these outcomes are 0.4x0.4x0.4 and 0.5x0.5x0.5
respectively, and these outcomes are independent the probability of
one or the other occurring is the sum of their individual probabilities and
0.4x0.4x0.4 + 0.5x0.5x0.5 = 0.189
As the results of each game are independent this is the product of thed) the probability A wins the first two games, and not the third.
probabilities of the required outcomes of each game. The probability that
A wins a game is 0.4, the probability that A does not win a game is 1-0.4=0.6.
So the required probability is 0.4x0.4x0.6=0.096