At Litchfield College of Nursing, 84% of incoming freshmen nursing students are

Question

At Litchfield College of Nursing, 84% of incoming freshmen nursing students are female and 16% are male. Recent records indicate that 70% of the entering female students will graduate with a BSN degree, while 80% of the male students will obtain a BSN degree. If an incoming freshman nursing student is selected at random, find the following probabilities. (Enter your answers to three decimal places.) P(student will graduate | student is female) P{student will graduate and student is female) P{student will graduate | student is male) P{student will graduate and student is male) P(student will graduate). Note that those who will graduate are either males who will graduate or females who will graduate. The events described the phrases "will graduate and is female" and "will graduate, given female" seem to be describing the same students. Why are the probabilities P(will graduate and is female) and P(will graduate | female) different? The term given refers to the sample space of all students, while the term and refers to restricting the sample space to females only. This is by chance. These probabilities are typically the same. These probabilities are the same. The term and refers to the sample space of all students, while the term given refers to restricting the sample space to females only.

Explanation / Answer

Let

G = will graduate
F = female
M = male

a)

P(G|F) = 0.70 [ANSWER, GIVEN]

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b)

P(G n F) = P(G|F) P(F) = 0.70*0.84 = 0.588 [ANSWER]

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c)

P(G|M) = 0.80 [ANSWER, GIVEN]

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d)

P(G n M) = P(G|M) P(M) = 0.80*0.16 = 0.128 [ANSWER]

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e)

P(G) = P(G n M) + P(G n F) = 0.128 + 0.588 = 0.716 [ANSWER]

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f)

OPTION D: The term and refers to the sample space of all students , while the term given refers to restricting the sample space to females only.

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