Normal
Sara’s volleyball team has white jerseys and green jerseys. The probability of wearing a white jersey to a game is the same as the probability of wearing a green jersey. Sara drew a tree diagram to calculate all the possible outcomes for wearing jerseys to three games.
White in Game 1 has white in game 2 and further has white and green as outcomes in game 3, the green outcome in game 2 further has white and green outcomes at game 3. The green in game 1 has white in game 2 and further has white and green as outcomes in game 3, the green outcome in game 2 further has white and green outcomes in game 3.
What is the probability that she will wear her green jersey for three games in a row?
A.1/3
B.1/2
C.1/8
D.1/6
The probability of wearing a green jersey in one game is 1/2 (since it is the same as the probability of wearing a white jersey). Now, since we want to know the probability of wearing a green jersey for three games in a row, we need to multiply the probabilities of wearing a green jersey for each of the three games.
So, the probability of wearing a green jersey for three games in a row is 1/2 x 1/2 x 1/2 = 1/8.
Therefore, the answer is (C) 1/8.
To calculate the probability that Sara will wear her green jersey for three games in a row, we need to look at the possible outcomes from the tree diagram that she drew.
From the diagram, we can see that there are two possibilities for the first game: either Sara wears a white jersey or a green jersey.
If she wears a white jersey for the first game, then for the second game, she has three possibilities: white, white, or green. And for the third game, she has two possibilities: white or green. So, in this case, she can wear her green jersey for three games in a row in 2 out of the 6 possible outcomes.
If she wears a green jersey for the first game, then for the second game, she also has three possibilities: white, white, or green. And for the third game, she has two possibilities: white or green. So, in this case, she can wear her green jersey for three games in a row in 2 out of the 6 possible outcomes.
Therefore, the total number of outcomes where Sara wears her green jersey for three games in a row is 2 + 2 = 4.
Since Sara's probabilities of wearing a white jersey and a green jersey are the same, the total number of possible outcomes is 6, which represents all the possible combinations of jerseys for the three games.
So, the probability that Sara will wear her green jersey for three games in a row is 4/6, which simplifies to 2/3.
Therefore, the correct answer is A. 1/3.
To calculate the probability that Sara will wear her green jersey for three games in a row, we need to look at the possible outcomes in the tree diagram.
The probability of wearing a green jersey in each game is the same as wearing a white jersey, which means each outcome has a probability of 1/2.
From the tree diagram, we can see that there are three possible outcomes where Sara wears her green jersey for three games in a row:
1. Green in game 1, green in game 2, green in game 3
2. Green in game 1, white in game 2, green in game 3
3. White in game 1, green in game 2, green in game 3
Therefore, the probability of Sara wearing her green jersey for three games in a row is 3/8.
So the correct answer is:
C. 1/8