Can someone guide me with this question?
Four teachers and five students have volunteered to serve on the school's fundraising committee, which is chaired by the principal. The principal wishes to select the committee using a random draw. He places each person's name on a slip of paper and draws four names.
a) What is the probability that atleast one teacher is on the committee?
how do you figure out if there is x amount of women, how many men there are? :S Help please, I have a quiz tomorrow :(
see other post.
What other post?
Anyone help?
To solve this question, we need to calculate the probability that at least one teacher is chosen for the committee.
Let's start by finding the total number of ways the committee can be formed. Since there are four positions on the committee, we can calculate this using combinations. We have 9 people in total (4 teachers + 5 students), and we want to choose 4 of them for the committee, so the total number of ways is:
C(9, 4) = 9!/(4!(9-4)!) = 9!/(4!5!) = (9*8*7*6)/(4*3*2*1) = 126
Next, let's find the number of ways the committee can be formed without any teacher. In this case, we only have students to choose from. So, the number of ways to choose 4 student committee members from 5 students is:
C(5, 4) = 5!/(4!(5-4)!) = 5!/(4!1!) = (5*4*3*2)/(4*3*2*1) = 5
To find the number of ways the committee can be formed with at least one teacher, we subtract the number of ways with no teacher from the total number of ways:
Number of ways with at least one teacher = Total number of ways - Number of ways with no teacher
= 126 - 5
= 121
Therefore, the probability that at least one teacher is on the committee is given by:
Probability = Number of ways with at least one teacher / Total number of ways
= 121/126
= 0.9603 (rounded to four decimal places)
So, the probability that at least one teacher is selected for the committee is approximately 0.9603.
Now, let's address your second question about finding the number of men based on the number of women. To determine the number of men given a certain number of women, you need to have additional information about the total number of people or the ratio of men to women. Without more information, it is not possible to determine the exact number of men.