Question

Employment data at a large company reveal that

72​%

of the workers are​ married,

52​%

are college​ graduates, and

three fourthsthree fourths

of the college grads are married. Complete parts a through c below.

​a) What's the probability that a randomly chosen worker is neither married nor a college​ graduate?

nothing

​(Type an integer or a decimal. Do not​ round.)

​b) What's the probability that a randomly chosen worker is married but not a college​ graduate?

nothing

​(Type an integer or a decimal. Do not​ round.)

​c) What's the probability that a randomly chosen worker is married or a college​ graduate?

nothing

​(Type an integer or a decimal. Do not​ round.)

        More

Answer 1

P(Married) = 0.72

P(Graduates) = 0.52

P(Married | Graduates) = 3/4 = 0.75

a)

P(Married | Graduates) = P(Married and Graduates) / P(Graduates) = 0.75

P(Married and Graduates) = 0.75 * 0.52 = 0.39

P(Married or Graduates) = P(Married) +  P(Graduates) - P(Married and Graduates)

= 0.72 + 0.52 - 0.39

= 0.85

Probability that a randomly chosen worker is neither married nor a college​ graduate = 1 - P(Married or Graduates)

= 1 - 0.85

= 0.15

b)

Probability that a randomly chosen worker is married but not a college​ graduate

= P(Married) - P(Married and Graduates)

= 0.72 - 0.39

= 0.33

c)

Probability that a randomly chosen worker is married or a college​ graduate = P(Married or Graduates)

= 0.85