Question

It is estimated that 26% of all California adults are college graduates and that 31% of California adults are regular internet users. It is also estimated that 21% of California adults are both college graduates and regular internet users. (a) What is the probability that a California adult is an internet user, given that he or she is a college graduate? Round your answer to 2 decimal places. (b) Among California adults, what is the probability that a randomly chosen internet user is a college graduate? Round your answer to 2 decimal places.

Answer 1

Answer:

a) There is an 81% probability that a California adult is an internet user, given that he or she is a college graduate.

b) There is a 68% probability that a randomly chosen internet user is a college graduate.

Step-by-step explanation:

The best way to solve this problem is building the Venn Diagram of these sets.

I am going to say that

A is the percentage of California adults that are college graduates.

B is the percentage of California adults that are regular internet users.

We have that:

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

In which a are those who are only college graduates and $(A \cap B)$ are those who are both college graduates and regular internet users.

By the same logic, we have that:

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

In which b are those who are only regular internet users and $(A \cap B)$ are those who are both college graduates and regular internet users.

We start finding these values from the intersection:

It is also estimated that 21% of California adults are both college graduates and regular internet users. This means that $A \cap B = 0.21$

26% of all California adults are college graduates. This means that $A = 0.26$

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

$0.26 = a + 0.21$

$a = 0.05$

31% of California adults are regular internet users. This means that $B = 0.31$

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

$0.31 = b + 0.21$

$b = 0.10$

(a) What is the probability that a California adult is an internet user, given that he or she is a college graduate?

The set of college graduates and regular internet users is given by $A \cap B$.

The set of college graduates is given by $A$.

So

$P = \frac{0.21}{0.26} = 0.81$

There is an 81% probability that a California adult is an internet user, given that he or she is a college graduate.

b) Among California adults, what is the probability that a randomly chosen internet user is a college graduate?

The set of college graduates and regular internet users is given by $A \cap B$.

The set of internet users in given by $B$.

So

$P = \frac{0.21}{0.31} = 0.68$

There is a 68% probability that a randomly chosen internet user is a college graduate.