Question

In a random sample of UTC students, 50% indicated they are Business majors, 40% Engineering majors, and 10% Other majors. Of the Business majors, 50% were females; whereas 25% of Engineering majors were females. Finally, 40% of the Other majors were female. Find the following and briefly show your calculation: a. What percentage of students in this sample was female? b. Given that a person is female, what is the probability that she is a business major?

Answer 1

Using conditional probability, it is found that:

a. 39% of students in this sample was female.

b. 64.1% probability that she is a business major.

What is Conditional Probability?

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

• P(B|A) is the probability of event B happening, given that A happened.

• $P(A \cap B)$ is the probability of both A and B happening.

• P(A) is the probability of A happening.

Item a:

The proportion associated with female students is given by:

• 50% of 50%(Business majors).

• 25% of 40%(Engineering majors).

• 40% of 10%(Other majors).

Hence:

P(A) = 0.5(0.5) + 0.25(0.4) + 0.4(0.1) = 0.39.

0.39 = 39% of students in this sample was female.

Item b:

The events related to the conditional probability are:

• Event A: Female.

• Event B: Business major.

Hence:

$P(A \cap B) = 0.5(0.5) = 0.25$

And the conditional probability is:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.25}{0.39} = 0.641$

0.641 = 64.1% probability that she is a business major.

You can learn more about conditional probability at https://brainly.com/question/14398287