Question

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?

Answer 1

a) 113/300

b) 1/2

c) 187/300

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