Question

2. The following table shows the probability of females and males preferring to drive an SUV or a sports car.(a) Are being male and preferring to drive a sports car independent or not independent? Show allcalculations to support your answer. Round answer to nearest hundredth. Be sure to answer thequestionLet A = being a maleLet B = preferring to drive a sports carAnswer:(b) Are being female and preferring to drive an SUV independent or not independent? Show allcalculations to support your answer. Round answer to nearest hundredth. Be sure to answer thequestionLet A = being a femaleLet B = preferring to drive an SUV

Answer 1

Being a male and preferring to drive a sports car represents dependent events because being a male influence the event of preferring a sports car, according to the chart.

Hence, A and B are dependent events.

To demonstrate this, we have to use the following formula

$P(A\cap B)=P(A)\cdot P(B)$

Where,

$\begin{gathered} P(A\cap B)=0.16 \\ P(A)=0.25 \\ P(B)=0.35 \end{gathered}$

Then

$\begin{gathered} 0.16=0.25\cdot0.35 \\ 0.16=0.0875 \end{gathered}$

Given that this result is not true. We prove that the events are not independent.

Now, let's do the same process to answer (b).

$P(A\cap B)=P(A)\cdot P(B)$

Where

$\begin{gathered} P(A)=0.75 \\ P(B)=0.65 \\ P(A\cap B)=0.56 \end{gathered}$

Then

$\begin{gathered} 0.56=0.75\cdot0.65 \\ 0.56=0.4875 \end{gathered}$

Hence, A and B are dependent events.