A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. (Hint: There are 10 possible samples.).
I really don't know where to begin
To find the possible samples of size three, we can use combinations. The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
Where n is the number of items to choose from, and r is the number of items to choose.
In this problem, n = 5 (people) and r = 3 (committee members). Plugging in these values into the formula, we get:
C(5, 3) = 5! / (3!(5-3)!)
= 5! / (3!2!)
= (5 * 4 * 3 * 2 * 1) / (3 * 2 * 1 * 2 * 1)
= 10
So there are 10 possible samples of size three that can be chosen from the group of five people.
Now let's list these possible samples:
1. A, B, C
2. A, B, D
3. A, B, E
4. A, C, D
5. A, C, E
6. A, D, E
7. B, C, D
8. B, C, E
9. B, D, E
10. C, D, E
From this list, we can see that B is included in 3 out of the 10 samples: (1) A, B, C, (2) A, B, D, and (3) A, B, E.
Therefore, the probability that B is included in the sample is 3/10, or 0.3.
No worries! I can help you with that problem. Let's break it down step by step.
First, let's list all the possible samples of size three that can be taken from the five people: A, B, C, D, E.
To determine all the possible samples, we can list all the combinations of three people that can be taken from the group of five. Here are all the possible combinations:
1. A, B, C
2. A, B, D
3. A, B, E
4. A, C, D
5. A, C, E
6. A, D, E
7. B, C, D
8. B, C, E
9. B, D, E
10. C, D, E
Now, to find the probability that B is included in the sample, we need to determine how many of these samples include B.
From the list, we can see that out of the 10 possible samples, B is included in 3 of them:
1. A, B, C
2. A, B, D
3. A, B, E
Therefore, the probability of selecting a sample that includes B is 3 out of 10 or 3/10.
So, the probability that B is included in the sample is 3/10.
I hope this explanation helps you understand how to approach the problem! If you have any further questions, feel free to ask.
what, you cannot list the samples of size 3?
ABC
ABD
ABE
...