Employment data at a large company reveal that 59% of the workers are married, that 20% are college graduates, and 1/6 of the college grads are married. What's the probability that a randomly chosen worker a) is neither married nor a college graduate? b) is married but not a college graduate? c) is married or a college graduate?

Question

Adelaide Patton

Mathematics

9 November, 06:12

Employment data at a large company reveal that 59% of the workers are married, that 20% are college graduates, and 1/6 of the college grads are married. What's the probability that a randomly chosen worker a) is neither married nor a college graduate? b) is married but not a college graduate? c) is married or a college graduate?

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Answers (1)

Know the Answer?

Jaelyn Watson · Answer 1

a) 113/300

b) 1/2

c) 187/300

Step-by-step explanation:

Lets call the events like follows:

a = married workers

b = graduate workers.

Then, a∧b = married and graduate workers.

We have:

p (a) = 59/100 (59%)

p (b) = 20/100 = 2/10 = 1/5 (20%)

p (a∧b) = 1/6.

So,

answer a) the probability to be neither married nor a college graduate is 1-p (aUb) = 1 - (p (a) + P (b) - P (a∩B)) = 1-59/100-1/5+1/6 = 113/300

answer b) the probability to be married but not a college graduate = p (a) ∩ (1-p (b)) = 59/100 x (1-20/100) = 1/2

answer c) the probability to be married or a college graduate p (a∪b) = p (a) ∪ p (b) - P (a∩B) = 59/100+1/5-1/6 = 187/300