Question

You randomly choose an undergraduate student from a large state university. Let E be the event that the student is male, let F be the event that the student is an in-state student, and let G be the event that the student is at least 20 years old. If these three events are probabilistically independent, and if P(E) = 0.48, P(F) = 0.72, and P(G) = 0.55, which of the following is true (to the nearest three decimals)?

a. P(student is an in-state male younger than 20) = 0.156
b. P(student is an out-of-state female younger than 20) = 0.168
c. P(student is an in-state female younger than 20) = 0.156
d. P(student is an out-of-state male at least 20) = 0.060

Answer 1

( a ) is the right answer .

Explanation:

P(E) = 0.48

Probability of being male = .48

Probability of being female = .52

P(F) = 0.72

Probability of being in state = .72

Probability of being out of state = .28

P(G) = 0.55

Probability of being in at least 20 years = .55

Probability of being less than 20 = .45

a )

P(student is an in-state male younger than 20)

= .72 x .48 x .45 = .1555 = .156

b )

P(student is an out-of-state female younger than 20)

= .28 x .52 x .45

= .065

c )

P(student is an in-state female younger than 20)

= .72 x .52 x .45 = .168

d )

P(student is an out-of-state male at least 20)

= .28 x .48 x .55 = .074

So , ( a ) is the right answer .