a box contains 3 red,2 blue,and 1 yellow marble. john picks a marble, does not put it replace it, then his brother tom picks a marble make a probability tree for the outcomes
Cannot make probability tree on these posts.
Sure! We can create a probability tree to represent the outcomes of John and Tom choosing a marble from the box.
Step 1: John Picks a Marble
There are three possible outcomes for John picking a marble:
- Outcome 1: John picks a red marble
- Outcome 2: John picks a blue marble
- Outcome 3: John picks a yellow marble
Step 2: Tom Picks a Marble
For each outcome in Step 1, there are different possibilities for Tom picking a marble:
- Outcome 1: John picks a red marble
- If John picks a red marble, there are now 2 red, 2 blue, and 1 yellow marble left in the box.
- Tom can pick any of these 5 remaining marbles, so there are 5 possible outcomes.
- Outcome 2: John picks a blue marble
- If John picks a blue marble, there are now 3 red, 1 blue, and 1 yellow marble left in the box.
- Tom can pick any of these 5 remaining marbles, so there are 5 possible outcomes.
- Outcome 3: John picks a yellow marble
- If John picks a yellow marble, there are now 3 red, 2 blue, and 0 yellow marble left in the box.
- Tom can only pick one of the remaining 5 marbles (1 red and 4 blue), so there are 5 possible outcomes.
To visualize this in a probability tree, we can draw a tree structure with the outcomes of each step branching out from the previous outcome. Each branch represents a different possibility:
John
/ | \
Red Blue Yellow
/ | \ / \
... ... ... ...
The number of branches coming out of each outcome depends on the number of possible outcomes for the next step.
I hope this helps! Let me know if you have any further questions.
To create a probability tree for the outcomes of John and Tom picking marbles from the box, we need to consider the possible choices and the associated probabilities at each step.
First, we start with John picking a marble. There are 3 red marbles, 2 blue marbles, and 1 yellow marble in the box. So the probability of John picking a red marble is 3/6, blue marble is 2/6, and yellow marble is 1/6. We can represent these probabilities on the probability tree as branches stemming from a "John" node.
Next, we consider Tom's choice, which is dependent on John's pick. For each of John's possible choices (red, blue, or yellow), we need to calculate the probabilities of what Tom picks. If John picks a red marble, there are now 2 red, 2 blue, and 1 yellow marble left in the box. Therefore, the probability of Tom picking a red marble is 2/5, blue marble is 2/5, and yellow marble is 1/5. We represent these probabilities on the probability tree as branches stemming from the respective John's choice branches.
Similarly, if John picks a blue marble, there will be 3 red, 1 blue, and 1 yellow marble left in the box. The probabilities of Tom picking a red marble, blue marble, or yellow marble will be 3/5, 1/5, and 1/5, respectively. These probabilities are represented as branches stemming from the blue branch of John's choice on the probability tree.
Finally, if John picks a yellow marble, there will be 3 red, 2 blue, and 0 yellow marbles left in the box. Tom's possibilities will be 3/5 for a red marble, 2/5 for a blue marble, and 0/5 (which is 0) for a yellow marble. These probabilities are represented as branches stemming from the yellow branch of John's choice on the probability tree.
By representing the probabilities on a probability tree, you can visually see the different outcomes and their associated probabilities.