Question

Records at the UH library show that 12% of all UH students check out books on history, 28% of all UH students check out books on science, and 6% check out books on both history and science. What is the probability that a randomly selected UH student checks out a history book or a science book or both?

Answer 1

Answer:

There is a 34% probability that a randomly selected UH student checks out a history book or a science book or both.

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a UH student checks out books on history.

B is the probability that a UH students checks out books on science.

We have that:

$A = a + (A \cap B)$

In which a is the probability that a UH student checks a book on history but not on science and $A \cap B$ is the probability that a UH student checks books both on history and science.

By the same logic, we have that:

$B = b + (A \cap B)$

What is the probability that a randomly selected UH student checks out a history book or a science book or both?

$P = a + b + (A \cap B)$

We start finding these values from the intersection.

6% check out books on both history and science. So $A \cap B = 0.06$

28% of all UH students check out books on science. So $B = 0.28$

$B = b + (A \cap B)$

$0.28 = b + 0.06$

$b = 0.22$

12% of all UH students check out books on history

$A = a + (A \cap B)$

$0.12 = a + 0.06$

$a = 0.06$

So

$P = a + b + (A \cap B) = 0.06 + 0.22 + 0.06 = 0.34$

There is a 34% probability that a randomly selected UH student checks out a history book or a science book or both.