Question

In a class of 50 students, 22 are Democrats, 14 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.

Answer 1

To find the probability of choosing a Democrat or a business major, first add the groups together, subtract the overlap, and divide by the total to obtain 60%.

Step-by-step explanation:

To solve the probability question, we need to determine the probability of choosing either a Democrat or a business major. Since some business majors are also Democrats, we can't simply add the two probabilities together; we must exclude the overlap to avoid double-counting.

Here's the process:

• First, find the total number of Democrats and business majors regardless of their other affiliations: 22 (Democrats) + 14 (business majors) = 36.
• Next, subtract the number that are both: 36 - 6 (Democrat business majors) = 30 unique students.
• Finally, calculate the probability: 30 (unique students who are either Democrats or business majors) / 50 (total number of students) = 0.60 or 60%.

Therefore, the probability of randomly selecting either a Democrat or business major from the class is 60%.

Answer 2

The probability P(D/ B) (choosing a Democrat or a business major) is 0.6.

How the probability is calculated

D be the set of Democrats,

B be the set of business majors,

n(D) be the number of Democrats,

n(B) be the number of business majors,

n(D/B) be the number of students who are both Democrats and business majors.

The probability P(D/ B) (choosing a Democrat or a business major) is given by:

P(D/ B) = (n(D) + n(B) - n(D/ B)/Total number of students

Substitute the given values:

P(D/ B) = (22 + 14 - 6)/50

= 30/50

= 0.6

The probability P(D/ B) (choosing a Democrat or a business major) is 0.6.