Question

team a and team b play a game of volleyball (which consists of 3 sets) and team a has a 2/3 chance of winning a set. if whichever team wins 2 sets wins the game, what is the probability that team a wins the game?

Answer 1

To find the probability that Team A wins the volleyball game, calculate the sum of probabilities for all the possible winning combinations, which results in a final probability of 20/27 that Team A wins the game.

Step-by-step explanation:

The question asks for the probability that Team A wins the volleyball game given that they have a 2/3 chance of winning a single set and the game is best of three sets. To determine this, we will consider all the possible ways Team A can win the game:

• Team A wins the first two sets (2/3 * 2/3)
• Team A wins the first and the third set (2/3 * 1/3 * 2/3)
• Team A loses the first set but wins the next two (1/3 * 2/3 * 2/3)

To find the total probability, we add these probabilities together:

P(Team A wins game) = (2/3 * 2/3) + (2/3 * 1/3 * 2/3) + (1/3 * 2/3 * 2/3) = 4/9 + 4/27 + 4/27 = 4/9 + 8/27 = 12/27 + 8/27 = 20/27

The final probability that Team A wins the game is 20/27.