a. A box contains three white balls and two red balls. A ball is drawn at random from the box and not replaced. Then a second ball is drawn from the box. Draw a tree diagram for this experiment and find the probability that the two balls are of different colors
b. Suppose that a ball is drawn at random from the box in part (a), its color is recorded, and then the ball is put back in the box. Draw a tree diagram for this experiment and find the probability that the two balls are of different colors.
a. Tree diagram:
W R
/ \ / \
W R W R
/ \ / \
W W R W
To find the probability that the two balls are of different colors, we can calculate the probability for each branch where the balls are of different colors and then add them up.
The probability of drawing a white ball first is 3/5.
For the branch where a white ball is drawn first, the probability of drawing a red ball second is 2/4.
So, the probability for this branch is (3/5) * (2/4) = 6/20.
The probability of drawing a red ball first is 2/5.
For the branch where a red ball is drawn first, the probability of drawing a white ball second is 3/4.
So, the probability for this branch is (2/5) * (3/4) = 6/20.
Adding up these probabilities, we get:
(6/20) + (6/20) = 12/20 = 3/5.
Therefore, the probability that the two balls are of different colors is 3/5.
b. Tree diagram:
W R
/ \ / \
W R W R
/ \ / \
W W R W
If the ball is put back in the box after it is drawn, then the probabilities for each branch remain the same.
Using the same calculations as in part (a), we find:
(3/5) * (2/5) + (2/5) * (3/5) = 12/25 + 12/25 = 24/25
Therefore, the probability that the two balls are of different colors is 24/25.
a. To draw a tree diagram for this experiment:
Step 1: Start with the first ball being drawn
- The branches will represent the two possible outcomes: white or red
- Assign probabilities to each branch based on the number of white and red balls in the box
- Label each branch with the corresponding color
Step 2: For each branch from step 1, draw another set of branches representing the second ball being drawn
- The branches will again represent the two possible outcomes: white or red
- Assign probabilities to each branch based on the remaining number of white and red balls in the box
- Label each branch with the corresponding color
The resulting tree diagram should have four branches at the second level, representing the four possible combinations of ball colors.
To find the probability that the two balls are of different colors, you need to identify the branches where the balls are of different colors and sum up their probabilities. In this case, there are two such branches: white-red and red-white. Add up their probabilities and you will have your answer.
b. To draw a tree diagram for this modified experiment:
Step 1: Start with the first ball being drawn
- The branches will represent the two possible outcomes: white or red
- Assign probabilities to each branch based on the number of white and red balls in the box
- Label each branch with the corresponding color
Step 2: For each branch from step 1, draw another set of branches representing the second ball being drawn
- The branches will again represent the two possible outcomes: white or red
- Assign probabilities to each branch based on the original number of white and red balls in the box
- Label each branch with the corresponding color
Since, in this case, the ball is put back in the box after recording its color, the probabilities for the second ball being drawn will be the same as in step 1.
The resulting tree diagram should look identical to the one in part (a), with four branches at the second level representing the four possible combinations of ball colors.
To find the probability that the two balls are of different colors, you need to identify the branches where the balls are of different colors and sum up their probabilities. In this case, the branches white-red and red-white will have the same probabilities as in part (a). Add up their probabilities to get your answer.
I don't know how to draw a tree diagram on this message board. However, in a, remember that the number of balls is reduced after each pick.
http://www.google.com/search?client=safari&rls=en&q=math+tree+diagram&ie=UTF-8&oe=UTF-8
a. R then W = 2/5*3/4 = .3
W then R = 3/5*2/4 = .3
The either-or probability = sum of individual probabilities.
b. R then W = 2/5*3/5 = 6/25
W then R = 3/5*2/5 = 6/25