A bag contains 5 red balls and 7 green balls . A ball is picked at random , its color is noted and it is given out . The bag is shaken and a second selection is made. A. Draw. Tree diagram to illustrate thr information. B. Calculate the probability that both balls are red
ball is not returned...
prob(both red) = (5/12)(4/11) = 5/33
A. To draw a tree diagram, we can start with the first selection and then branch out to the second selection:
First selection:
- Red ball: (5/12 chance)
- Green ball: (7/12 chance)
Second selection (conditional probabilities):
- If the first selection is a red ball:
- Red ball: (4/11 chance)
- Green ball: (7/11 chance)
- If the first selection is a green ball:
- Red ball: (5/11 chance)
- Green ball: (6/11 chance)
Here's a visual representation of the tree diagram:
|--- Red ball: (4/11) --- Red ball: (0/10)
|
Red ball: (5/12)|
|
|--- Red ball: (5/11) --- Green ball: (6/10)
|
|
|--- Green ball: (7/12) --- Red ball: (5/11)
|
|
|--- Green ball: (6/11) --- Red ball: (5/10)
|
|
|--- Green ball: (7/11) --- Green ball: (6/10)
B. To calculate the probability that both balls are red, we need to multiply the probabilities of each selection:
Probability of first selection being red: 5/12
Probability of second selection being red (given the first selection was red): 4/11
So, the probability that both balls are red is (5/12) * (4/11) = 20/132 = 5/33.
Therefore, the probability that both balls selected are red is 5/33.
To answer part A of the question, we can draw a tree diagram to illustrate the information.
The first level of the tree diagram will have two branches: one for picking a red ball and one for picking a green ball. The second level will have two branches for each possibility from the first level, representing the second selection. Finally, the third level will represent the color of the second ball.
Here is a tree diagram illustrating the information:
R G
/ \ / \
R G R G
/ \ / \ / \ / \
R G R G R G R G
Now, let's move on to part B and calculate the probability that both balls are red.
To find the probability of two events occurring together, we can multiply their individual probabilities.
The probability of picking a red ball on the first selection is 5 out of 12 (since there are 5 red balls and 12 balls in total).
After the first selection, we are left with 4 red balls and 11 balls in total, so the probability of picking a red ball on the second selection is 4 out of 11.
To find the probability of both events occurring together (picking red twice), we multiply the probabilities:
(5/12) * (4/11) = 20/132 = 5/33
Therefore, the probability of picking two red balls is 5/33.