How to find the probabilty in this question?

Question

At a convention there are 7 maths instructors and 5 computer science
instructors. The probability of randomly selecting a maths instructor or
a computer science instructor is 1112. Determine the probability of randomly
selecting an instructor that teaches both maths and computer science.

should i use addition rule? or what shud i do?

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Answer 1 · 2018-07-12T01:14:42

#1/12#, which is about 8.3%.

We will use the rule

#P(A uu B) = P(A) + P(B) - P(A nn B)#

Let A be the event that a person selected is a math teacher.
Let B be the event that a person selected is a computer science teacher.

Of the 12 people at the convention, 11 of them teach at least one of math or computer science. Meaning

#P(A uu B) = 11/12#

We also know 7 of the people are math teachers, so

#P(A) = 7/12#

And since 5 of the people are computer science teachers, we know

#P(B) = 5/12#

Plugging these all into the first equation gives us

#11/12 = 7/12 + 5/12 - P(A nn B)#

Now we just solve for #P(A nn B)#:

#P(A nn B) = 7/12 + 5/12 - 11/12 = 1/12#

So the probability of choosing someone who teaches both math and computer science is #1/12#, which is about 8.3%.