Asurvey found that 73% of adults have a landline at their residence (event a); 83% have a cell phone (event b). it is known that 2% of adults have neither a cell phone nor a landline. 3. what is the probability that an adult selected at random has both a landline and a cell phone? a. 0.58 b. 0.98 c. 0.6059 d. none of these work: 4. given an adult has a cell phone, what is the probability he does not have a landline?
a. 0.27
b. 0.25
c. 0.3012
d. none of these

3. What is the probability that an adult selected at random has both a landline and a cell phone?

A. 0.58

4. Given an adult has a cell phone, what is the probability he does not have a landline?

C. 0.3012

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 an adult has a landline at his residence.

B is the probability that an adult has a cell phone.

C is the probability that a mean is neither of those.

We have that:

In which a is the probability that an adult has a landline but not a cell phone and is the probability that an adult has both of these things.

By the same logic, we have that:

The sum of all the subsets is 1:

2% of adults have neither a cell phone nor a landline.

This means that .

73% of adults have a landline at their residence (event A); 83% have a cell phone (event B)

So .

What is the probability that an adult selected at random has both a landline and a cell phone?

This is .

We have that . So

By the same logic, we have that:

.

So

So the answer for question 3 is A.

4. Given an adult has a cell phone, what is the probability he does not have a landline?

83% of the adults have a cellphone.

We have that

25% of those do not have a landline.

So

The answer for question 4 is C.