If a 3�]person committee is selected at random, what is the probability that
Republicans make up the majority?
Lacking data. What is the makeup of the group they are selected from?
To solve this problem, we need to calculate the total number of possible outcomes and the number of favorable outcomes.
Step 1: Calculate the total number of possible outcomes.
If we have a 3-person committee, each person can either be a Republican or not. Since there are only two options for each person, the total number of possible outcomes is 2^3, which is equal to 8.
Step 2: Calculate the number of favorable outcomes.
To have Republicans make up the majority, we can consider two cases:
Case 1: There are 2 Republicans and 1 non-Republican.
The number of ways to choose 2 out of 3 Republicans is given by the combination formula: C(3,2) = 3.
For the remaining position, we can choose any of the non-Republicans, which gives us 1 option.
So, the total number of favorable outcomes in this case is 3 * 1 = 3.
Case 2: There are 3 Republicans and 0 non-Republicans.
The number of ways to choose 3 out of 3 Republicans is given by the combination formula: C(3,3) = 1.
So, the total number of favorable outcomes in this case is 1.
Step 3: Calculate the total number of favorable outcomes.
To find the probability, we need to add up the number of favorable outcomes from each case: 3 + 1 = 4.
Step 4: Calculate the probability.
The probability of Republicans making up the majority is given by:
Number of favorable outcomes / Total number of possible outcomes = 4 / 8 = 1/2.
Therefore, the probability that Republicans make up the majority in a randomly selected 3-person committee is 1/2 or 0.5.