If Julie is offered the New Jersey job, what is the conditional probability that

Question

If Julie is offered the New Jersey job, what is the conditional probability that she is also offered the federal job? (Round your answer to two decimal places.) Here are the projected numbers (in thousands) of earned degrees in a certain country during an academic year, classified by level and by the sex of the degree recipient: Convert this to a table giving the probabilities for selecting a degree earned and classifying the recipient by gender and the degree by the levels given above. (Round your answers to four decimal places.) If you choose a degree recipient at random, what is the probability that the person you choose is a woman? (Round your answer to four decimal places.) What is the conditional probability that you choose a woman, given that the person chosen received a professional degree? (Round your answer to four decimal places.) Are the events "choose a woman" and "choose a professional degree recipient" independent? How do you know?

Explanation / Answer

7. a. Probability of each classification = Total number of people in that classification / total number of people

So, probabilities are given by:

b. P(Woman) = 0.2945 + 0.1334 + 0.0203 + 0.0129

= 0.4611

c. P(Woman | Professional) = P(Woman and Professional) / P(Professional)

= 0.0203 / (0.0203 + 0.0193) = 0.5126

d. No, because the two probabilities in (b) and (c) are not equal.

Bachelor's Master's Professional Doctorate Male 758/2017 = 0.3758 275/2017 = 0.1363 39/2017 = 0.0193 15/2017 = 0.0074 Female 594/2017 = 0.2945 269/2017 = 0.1334 41/2017 = 0.0203 26/2017 = 0.0129

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