Question

a 2018 pew research center survey found that more americans believe they could give up their televisions than could give up their cell phones (pew research website). assume that the following table represents the joint probabilities of americans who could give up their television or call phone. excel file: data04 - 37.xlsx

could give up television: yes

could give up television: no

could give up cellphone: yes

0.31

0.17

0.48

could give up cellphone: no

0.38

0.14

0.52

0.69

0.31

a. what is the probability that a person could give up their cell phone (to 2 decimals)?
b. what is the probability that a person who could give up their cell phone could also give up television (to 2 decimals)?
c. what is the probability that a person who could not give up their cell phone could give up television (to 2 decimals)?
d. is the probability a person could give up television higher if the person could not give up a cell phone or if the person could give up a cell phone? the probability a person could give up television if they could not give up a cellphone is higher than the probability a person could give up television if they could give up a cellphone.

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$.

Step2: Calculate the probability for part b

Let $A$ be the event of giving up television and $B$ be the event of giving up cellphone. We know that $P(A\cap B) = 0.31$ and $P(B)=0.48$. Then $P(A|B)=\frac{0.31}{0.48}\approx0.65$.

Step3: Calculate the probability for part c

Let $A$ be the event of giving up television and $B$ be the event of not - giving up cellphone. We know that $P(A\cap B) = 0.38$ and $P(B)=0.52$. Then $P(A|B)=\frac{0.38}{0.52}\approx0.73$.

Step4: Compare the probabilities for part d

The probability of giving up television given that a person can give up cellphone is approximately $0.65$. The probability of giving up television given that a person cannot give up cellphone is approximately $0.73$. So the probability a person could give up television if they could not give up a cellphone is higher.

Answer:

b. $0.65$
c. $0.73$
d. The probability a person could give up television if they could not give up a cellphone is higher.