Question

People were asked if they have cable TV at home. The people were divided by gender and the results are listed below. Yes No Male 59 72 Female 63 76 a)Find the probability that a person has cable TV at home. b)Find P(Yes | Female) c) Find P(Female | Yes)

Answer 1

ANSWER:

a) 0.45

b) 0.45

c) 0.52

STEP-BY-STEP EXPLANATION:

The first thing is to calculate the total of YES and the total of NO. In the same way the total of male and female.

$\begin{gathered} \text{Yes }=59+63=122 \\ \text{No }=72+76=148 \\ \text{Male }=59+72=131 \\ \text{Female }=63+76=139 \end{gathered}$

a)

The probability if the person has cable TV would be the proportion between the total of YES and the total number of people.

Just like that:

$P\text{ (has cable TV)=}\frac{122}{122+148}=\frac{122}{270}=0.45$

b)

The probability of having cable being female would be the proportion between the YES, are female and the total amount of female.

Just like that:

$P\text{ (Yes | Female) }=\frac{63}{139}=0.45$

c)

The probability of being female having a cable would be the proportion between the YES, are female and the total number of YES.

Just like that:

$P\text{ (Female| Yes) }=\frac{63}{122}=0.52$