Here are the projected numbers (in thousands) of earned degrees in a certain cou

Question

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:

(a) 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.)

(b) 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.)


(c) 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.)

(d) Are the events "choose a woman" and "choose a professional degree recipient" independent? How do you know?

Yes, because the two probabilities in (b) and (c) are equal.

Yes, because the two probabilities in (b) and (c) are not equal.    

No, because the two probabilities in (b) and (c) are equal.

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

Bachelor's Master's Professional Doctorate Female 776 348 44 18 Male 588 192 46 24

Explanation / Answer

(a)

Following is the completed table:

The probability of a cell is calculated as follows:

P= (cell value) / 1956

For example:

P=776 /1956

And following table shows the probability :

(b)

The probability that the person you choose is a woman is

P(woman) = 0.5756

(c)

P(professional) = 0.045

P(professional and woman) = 0.0199

P(woman | professional) = P(professional and woman) / P(professional) = 0.0199 /0.045 = 0.4422

(d)

Last option is correct.

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