John hs 3 red markers and 5 blue markers. What is the probability that he picks a red marker, and then, without replacing it, selects another red marker?
Please show me how to set this up (you don't have to give me the answer)...thank you
8 markers
3/8 times 2/7
since there is no replacement.. choosing from 7 and we have to assume that we got a red the first time which leaves 2 red.
To calculate the probability that John picks a red marker and then, without replacing it, selects another red marker, we need to divide the number of favorable outcomes by the total number of possible outcomes.
Let's start by calculating the number of favorable outcomes, i.e., the number of ways John can select a red marker and then another red marker without replacement.
Since John has 3 red markers, he can select the first red marker in 3 ways (assuming he randomly picks one of the red markers).
After he has selected the first red marker, he only has 2 red markers left. Therefore, for the second pick, he can select another red marker in 2 ways.
So, the number of favorable outcomes is 3 (for the first red marker) multiplied by 2 (for the second red marker).
Now, let's find the total number of possible outcomes, which is simply the total number of markers.
John has 3 red markers and 5 blue markers, so the total number of markers is 3 + 5 = 8.
Thus, the probability that John picks a red marker and then, without replacing it, selects another red marker is:
(Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
This probability can be written as (3 * 2) / 8.
You can simplify the expression further, but this is how you set up the calculation for the probability.
To determine the probability of John picking a red marker, and then, without replacing it, selecting another red marker, we can follow these steps to set up the problem:
Step 1: Determine the number of red markers John has. In this case, John has 3 red markers.
Step 2: Determine the number of blue markers John has. In this case, John has 5 blue markers.
Step 3: Calculate the probability of John picking a red marker as the first event. To do this, divide the number of red markers by the total number of markers:
- Probability of picking a red marker = Number of red markers / Total number of markers
- Probability of picking a red marker = 3 / (3 + 5)
Step 4: Calculate the probability of selecting another red marker, without replacing the first one. To do this, subtract the chosen red marker from the total markers and recalculate the probability:
- Probability of selecting another red marker = (Number of red markers - 1) / (Total number of markers - 1)
- Probability of selecting another red marker = (3 - 1) / (8 - 1)
Step 5: Multiply the probabilities of both events to find the probability of both events happening in sequence:
- Probability of picking a red marker and then selecting another red marker = Probability of picking a red marker × Probability of selecting another red marker
By following these steps, you can calculate the probability of John picking a red marker and then, without replacing it, selecting another red marker.