There are 8 speaking roles in the play. Of the 8 speaking roles, 5 are for males and 3 are for females. After the 8 speaking roles in the play are cast, the remaining cast members will make up the chorus.
C. What is the probability that the set of siblings consisting of a brother and his 2 sisters are all in the chorus?
How many are in the cast?
The question doesn't say that so that is why I'm confused & can't figure it out.
Part D. is asking & I don't understand the first part in order to answer this part.
Write an expression that represents the probability that the set of siblings that consists of a brother and his 2 sisters are all in the chorus?
You first started asking this question under the name of Gabs, now you are Amy
The above question is clearly based on some previous problem which we cannot see.
e.g. how can we possible know how many men and how many women are in the cast?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
1/5 * 2/3 = probability they are chosen for speaking roles.
Subtract from 1 to get chorus probability.
To calculate the probability that the set of siblings consisting of a brother and his 2 sisters are all in the chorus, we need to consider the total number of ways to distribute the siblings among the speaking roles and the chorus.
First, let's find the total number of ways to distribute the 8 speaking roles among the 5 males and 3 females. This can be calculated using combinatorics, specifically the concept of combinations.
The total number of ways to choose 5 males from a group of 5 is denoted as "5 choose 5" and can be calculated as C(5, 5) = 1.
Similarly, the total number of ways to choose 3 females from a group of 3 is "3 choose 3" and can be calculated as C(3, 3) = 1.
To find the total number of ways to distribute the siblings among the speaking roles, we need to multiply the number of ways to choose 5 males with the number of ways to choose 3 females. Therefore, the total number of distributions is 1 * 1 = 1.
Now, since the remaining cast members will make up the chorus, we have (8 - 5 - 3) = 0 roles left for the siblings to be in the chorus.
So, the probability that the set of siblings consisting of a brother and his 2 sisters are all in the chorus is 0, because there are no remaining roles available for them in the chorus.