According to reuters, a survey undertaken by the national center for health statistics revealed that about 25% of u. s. households have only a cell phone (no land line). according to the fcc, 65% of u. s. households have high-speed internet. suppose of u. s. households having only a cell phone, 80% have high-speed internet. a u. s. household is randomly selected.

a. what is the probability that the household has only a cell phone and has high-speed internet?
b. what is the probability that the household has only a cell phone or has high-speed internet?
c. what is the probability that the household has only a cell phone and does not have high-speed internet?
d. what is the probability that the household does not have just a cell phone and does not have high-speed internet?
e. what is the probability that the household does not have just a cell phone and does have high-speed internet?

a) P=0.8

b) P=0.67

c) P=0.05

d) P=0.33

e) P=0.45

Step-by-step explanation:

a. What is the probability that the household has only a cell phone and has high-speed Internet?

This probability is stated in the question: "Suppose of U.S. households having only a cell phone, 80% have high-speed Internet", so the probability is P=0.8.

b. What is the probability that the household has only a cell phone or has high-speed Internet?

This probability is equal to the sum of the probability of having only a cell phone and the probability of having high-speed internet, less the probability of having both (to avoid counting this household twice).

c. What is the probability that the household has only a cell phone and does not have high-speed Internet?

This is equal to the probability of not having high-speed internet given that it has a cell phone (complementaty of the proability of Point (a)) multiplied by the probability of having a cell phone.

d. What is the probability that the household does not have just a cell phone and does not have high-speed Internet?

This probability is complementary of the one calculated in Point (c).

e. What is the probability that the household does not have just a cell phone and does have high-speed Internet?

This is equal to the probability of having high-speed internet less the probability it has both (cell phone and internet).

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