A basketball team has to play 3 games in an elimination roumd. What is the probability of them winning?
A. 0 games
B. 1 game
C. 2 games
D. 3 games
What is the answer of getting a probability of 0 game?
no response
To calculate the probability of a basketball team winning a certain number of games in an elimination round with 3 games, we need to consider the total number of possible outcomes and the number of desired outcomes for each scenario.
There are a total of 2^3 = 8 possible outcomes because each game can have two possible outcomes - winning or losing.
A. 0 games: In this scenario, the team loses all three games. There is only one way for this to happen, so the probability is 1/8.
B. 1 game: In this scenario, the team wins one game and loses the other two. There are three possible ways for this to happen: WLL, LWL, or LLW (W denotes a win, and L denotes a loss). So the probability is 3/8.
C. 2 games: In this scenario, the team wins two games and loses one. There are three possible ways for this to happen: WWL, WLW, or LWW. So the probability is also 3/8.
D. 3 games: In this scenario, the team wins all three games. There is only one way for this to happen, so the probability is 1/8.
Therefore, the probabilities of winning are as follows:
A. 0 games: 1/8
B. 1 game: 3/8
C. 2 games: 3/8
D. 3 games: 1/8
To find the probability of the basketball team winning each possible number of games, we need to know the total number of possible outcomes.
In each game, there are two possible outcomes: the team can either win or lose. Therefore, for three games, the total number of possible outcomes is 2^3 = 8.
Now, let's calculate the probability for each possible number of wins:
A. 0 games: There is only one outcome where the team loses all three games, so the probability is 1/8.
B. 1 game: There are three outcomes where the team wins one game and loses the other two (WWL, WLW, LWW), so the probability is 3/8.
C. 2 games: There are three outcomes where the team wins two games and loses one (WWL, LWW, WLW), so the probability is also 3/8.
D. 3 games: There is only one outcome where the team wins all three games, so the probability is 1/8.
To summarize:
A. Probability of winning 0 games: 1/8
B. Probability of winning 1 game: 3/8
C. Probability of winning 2 games: 3/8
D. Probability of winning 3 games: 1/8