Question

the accompanying table shows the numbers of male and female students in a particular country who received bachelors degrees in business in a recent year. complete parts (a) and (b) below.

(a) find the probability that a randomly selected student is male, given that the student received a business degree.
the probability that a randomly selected student is male, given that the student received a business degree, is 0.520.
(round to three decimal places as needed.)

(b) find the probability that a randomly selected student received a business degree, given that the student is female.
the probability that a randomly selected student received a business degree, given that the student is female, is .
(round to three decimal places as needed.)

Explanation:

Identify the given values and target

Using the Conditional Probability Notation knowledge point
We are given a contingency table of business graduates:

• Female students with Business degrees: \(174,846\)
• Total Female students: \(1,084,300\)

We need to find the conditional probability:

$$ P(\text{Business Degree} \mid \text{Female}) $$

Apply the conditional probability formula

Using the Conditional Probability Notation knowledge point

$$ P(\text{Business Degree} \mid \text{Female}) = \frac{\text{Number of Female students with Business degrees}}{\text{Total number of Female students}} $$

Calculate the probability

Using the Conditional Probability Notation knowledge point

$$ P(\text{Business Degree} \mid \text{Female}) = \frac{174,846}{1,084,300} \approx 0.161252 $$

Round to three decimal places

Using the Conditional Probability Notation knowledge point

$$ 0.161252 \approx 0.161 $$

Answer:

(b) Find the probability that a randomly selected student received a business degree, given that the student is female.

The probability that a randomly selected student received a business degree, given that the student is female, is <blank>0.161</blank>.