Question

	bachelor’s	master's	professional	doctorate	total
female	933	402	51	26	1412
male	661	260	44	26	991
total	1594	662	95	52	2403

what’s the probability that a randomly selected degree earner

1. is female?

2. is female and the person has earned a professional degree?

3. is female or the person has earned a professional degree?

4. is female if the person earned a professional degree?

5. earned a professional degree if the person is female?

6. Does the gender/degree data above suggest that the variables binary gender and degree earned are

   1. Mutually exclusive? Explain,

   2. Independent? Explain.

Answer 1

a) P(female) = 1412 / 2403 = 0.5876

b) P(female and professional) = 51 / 2403 = 0.0212

c) P(female or professional) = P(female) + P(professional) - P(female and professional)

                                           = 1412/2403 + 95/2403 - 51/2403

                                           = 0.6059

d) P(female | professional) = P(female and professional) / P(professional) = (51/2403) / (95/2403) = 51/95 = 0.5368

e) P(professional | female) = P(female and professional) / P(female) = (51/2403) / (1412/2403) = 51/1412 = 0.0361

f) No, they are not mutually exclusive. Because P(female and professional) ≠ 0

g) No, they are not independent events. Because P(female | professional) ≠ P(female)