In a class of 50 students, 35 are Democrats, 17 are business majors, and 6 of the business majors are Democrats. If one student is randomly selected from the class, find the probability of choosing a Democrat or a business major.
35/50 + 17/50 - 6/50 =.92 which is 23/25
To find the probability of selecting a Democrat or a business major, we need to use the principle of inclusion-exclusion.
The total number of students in the class is 50.
The number of Democrat students is 35.
The number of business major students is 17.
The number of business major students who are also Democrats is 6.
To find the probability of selecting a Democrat or a business major, we need to find the total number of students who are Democrats or business majors, and then divide it by the total number of students.
First, let's find the number of students who are Democrats or business majors. We calculate this by adding the number of Democrats and the number of business majors and then subtracting the number of business major Democrats, since they were counted twice:
Number of students who are Democrats or business majors = Number of Democrats + Number of Business Majors - Number of Business Major Democrats
= 35 + 17 - 6
= 46
So, there are a total of 46 students who are either Democrats or business majors.
Now, we can calculate the probability of selecting a Democrat or a business major by dividing the number of students who are Democrats or business majors by the total number of students:
Probability of selecting a Democrat or a business major = Number of students who are Democrats or business majors / Total number of students
= 46 / 50
= 0.92 or 92%
Therefore, the probability of choosing a Democrat or a business major is 0.92 or 92%.
To find the probability of choosing a Democrat or a business major, we need to sum the probabilities of choosing a Democrat and a business major separately, and then subtract the probability of choosing a student who is both a Democrat and a business major. Let's break down the problem step-by-step:
Step 1: Find the probability of choosing a Democrat.
Out of the 50 students, 35 are Democrats. So, the probability of choosing a Democrat is 35/50.
Step 2: Find the probability of choosing a business major.
Out of the 50 students, 17 are business majors. So, the probability of choosing a business major is 17/50.
Step 3: Find the probability of choosing a student who is both a Democrat and a business major.
Out of the 6 business majors, all of them are Democrats. So, the probability of choosing a student who is both a Democrat and a business major is 6/50.
Step 4: Calculate the probability of choosing a Democrat or a business major.
To calculate this probability, we sum the probabilities of choosing a Democrat and a business major, and then subtract the probability of choosing a student who is both.
Probability(Democrat or business major) = Probability(Democrat) + Probability(business major) - Probability(Democrat and business major)
= 35/50 + 17/50 - 6/50
= 52/50
= 26/25
Therefore, the probability of choosing a Democrat or a business major is 26/25.