Teams named East and West are playing a best-2-out-of-3 series of games. This me

Question

Teams named East and West are playing a best-2-out-of-3 series of games. This means at the first team to win two games wins the series. (For example, in the NCAA College Baseball World Series, the two teams in the finals play a best-2-out-of-3 series.) If the first two games are won by the same team, the series is over. The 3rd game is played only if the teams are 1-1 after the first two games. In each game that is played, the probability that East wins is 0.6. So the probability West wins is 0.4. What is the probability that East wins the series? What is the probability that the series requires only two games? What is the probability that the team that wins the first game wins the series? What is the expected value for how many games are played? Teams named East and West are playing a best-2-out-or-3 series of games. This means that the first team to win two games wins the series. (For example, in the NCAA College Baseball World Series, the two teams in the finals play a best-2-out-of-3 series.) If the first two games are won by the same team, the series is over. The 3rd game is played only if the teams are 1-1 after the first two games. In each game that is played, the probability that East wins is rho. So the probability West wins is q = 1 - rho. Suppose the probability that the winner of the first game ends up winning the series 0.86. There are two different values of p for which this can be true. The smaller value of p which makes this can true is The large value of p which makes this true is Draw a tree diagram for the series of games played, and enter "p" or "q" on each branch of the tree. So for each possible outcome, you'll be able to express the probability of the outcome as a product of p's and q's. Write out the sum of the probabilities of all the outcomes where the winner of the series is the same team that wins the first game of the series. (So this will be a sum of terms involving p's and q's. Now replace very 'q' by "1 p" so that "p" is the only unknown, and simplify the expression as much as possible by combining terms. You'll wind up with a quadratic expression involving the unknown 'p'. Then set this expression equal to 0.86 and solve for the two values of p that satisfy this equation. If you're using the quadratic formula, then you'll get both values out of the quadratic formula. If you're sing a graphing tool, you'll simply be identifying the two places where a parabola intersects a straight line.

Explanation / Answer

Probability that East will win the game p = 0.6

Probabilityt that West will win the game q = 0.4

(A)

Probability that East wins the series = 0.6*0.6 + 0.4*0.6*0.6 + 0.6*0.4*0.6 = 0.648

Here we have considered the different ways where East will win 3 matches in order to win the series.

(B)

Here we want to find the probability of winning the series by either team in two games. This means first two games played will be won by either East or West

hence required probability = 0.6*0.6 + 0.4*0.4 = 0.52

(C)

Probability that Team wins the first game wins the series = 0.6*(0.6 + 0.4*0.6) + 0.4*(0.4 + 0.6*0.4) = 0.76

Here first expression is for when East wins the first game and in second expression when West wins the first game.

(D)

Expected number of games to be played are 2 to decide the winner for the series.

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