Question

People at the state fair were surveyed about which type of lemonade they preferred. The results are shown below. Pink lemonade: 156 males, 72 females Yellow lemonade: 104 males, 48 females The events "prefers pink lemonade" and "female" are independent because P(pink lemonade | female) = P(pink lemonade) = 0.6. P(female | pink lemonade ) = P(pink lemonade) = 0.3. P(pink lemonade | female) = 0.3 and P(pink lemonade) = 0.6. P(female | pink lemonade ) = 0.3 and P(pink lemonade) = 0.6.

Answer 1

P(pink lemonade | female) = P(pink lemonade) = 0.6.

Explanation:

A

Answer 2

`P(pink) = P(pink |\ female) = 0.6`

Explanation:

Given

`\begin{array}{ccc}{} & {Male} & {Female} & {Pink} & {156} & {72} \ \\ {Yellow} & {104} & {48} \ \end{array}`

Required

Why
`prefers\ pink\ lemonade` and
`female` are independent

First, calculate
`P(pink |\ female)`

This is calculated as:

`P(pink |\ female) = (n(pink\ \&\ female))/(n(female))`

`P(pink |\ female) = (72)/(48+72)`

`P(pink |\ female) = (72)/(120)`

`P(pink |\ female) = 0.6`

Next, calculate
`P(pink)`

`P(pink) = (n(pink))/(n(Total))`

`P(pink) = (156 + 72)/(156 + 72 + 104 + 48)`

`P(pink) = (228)/(380)`

`P(pink) = 0.6`

So, we have:

`P(pink) = P(pink |\ female) = 0.6`

Hence, they are independent