The following table shows the breakdown of gender and the hugest degree among a

Question

The following table shows the breakdown of gender and the hugest degree among a university's faculty. What is the probability that a randomly selected professor is a. Male and has a Doctorate b. Male or has a Masters degree c. Is a female given they have a Decorate d. Is gender and degree independent according to these results? Justify mathematically. A recent survey was done to see how many math classes students had completed when sophomore year. Below is the fictional results. Find the mean and standard deviation probability model. for credit.

Explanation / Answer

4 a) P(Male and has a Doctorate)

= 28 / 66

= 14 / 33

b) P(Male or has a Masters degree)

= P(Male) + P(Masters degree) - P(Male and masters degree)

= 46/66 + 26/66 - 18/66

= 54/66

= 9/11

c) P(Female | Doctorate)

= 12 / 40

= 3/10

d) If gender and degree would be independent then:

P(Female | Doctorate) should be equal to P(Female).

From part c),

P(Female | Doctorate) = 3 / 10

Also,

P(Female) = 20 / 66 = 10 / 33

Since the above two probabilities are not equal, gender and degree are dependent.

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