Question

One of these 100 students is selected at random to give more detailed answers to some follow-up questions. majoring in business another administration major taken a public speaking class 10 20 not taken a public speaking class 45 25 What is the probability that the chosen student has taken a public speaking class or is majoring in business administration?

Answer 1

To calculate the probability that the selected student has taken a public speaking class or is majoring in business administration, we need to use the concept of "union" in probability.

Let's denote:

A = Event that the student has taken a public speaking class.

B = Event that the student is majoring in business administration.

We are interested in finding P(A ∪ B), which represents the probability that either A or B (or both) occur.

To calculate P(A ∪ B), we can use the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Given the following information:

- P(A) = 20/100 (since 20 students have taken a public speaking class out of 100)

- P(B) = 10/100 (since 10 students are majoring in business administration out of 100)

- P(A ∩ B) = 0 (because the information about students who have both taken a public speaking class and are majoring in business administration is not provided)

Now we can substitute these values into the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

= 20/100 + 10/100 - 0

= 30/100

= 0.3

Therefore, the probability that the chosen student has taken a public speaking class or is majoring in business administration is 0.3, or 30%.