a bag contains 10 marbles of which 2 are red and 8 are black.Bag B contains 12 marbles of which 4 are ed and 8 are black.A ball is drawn at random from each bag.
5.1 draw a probability tree diagram to show possible outcome
So, did you draw the tree? Can't show you mine on this site.
Yed
Sure! Here's a probability tree diagram to show the possible outcomes:
Bag A Bag B
/ \ / \
Red Black Red Black
| | | |
P(Red) = 2/10 P(Red) = 4/12 P(Black) = 8/10 P(Black) = 8/12
Each branch represents a possible outcome, and the probabilities of each outcome are written next to the corresponding branches.
To draw a probability tree diagram for this scenario, follow these steps:
Step 1: Identify the possible outcomes for each bag.
- Bag A: There are 10 marbles, 2 of which are red and 8 are black.
- Bag B: There are 12 marbles, 4 of which are red and 8 are black.
Step 2: Draw the branches for each outcome.
- Start by drawing two branches coming from the initial node representing the two bags (A and B).
- On the branch for Bag A, draw two sub-branches representing the possible outcomes for Bag A (Red and Black).
- On the branch for Bag B, draw two sub-branches representing the possible outcomes for Bag B (Red and Black).
Step 3: Assign probabilities to each outcome.
- Since the selection is random, each outcome has a certain probability. In this case, you can assign the probabilities based on the number of marbles of each color in each bag.
- On the branch for Bag A, assign a probability of 2/10 (2 red marbles out of a total of 10) to the Red sub-branch, and a probability of 8/10 (8 black marbles out of a total of 10) to the Black sub-branch.
- On the branch for Bag B, assign a probability of 4/12 (4 red marbles out of a total of 12) to the Red sub-branch, and a probability of 8/12 (8 black marbles out of a total of 12) to the Black sub-branch.
Step 4: Label the branches and sub-branches.
- Label the initial node as "Bag A/B".
- Label the sub-branches as "Red" and "Black" for each bag.
The final probability tree diagram should show two initial branches (Bag A and Bag B), each with two sub-branches (Red and Black) labeled with their respective probabilities.