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

Answer:

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

Step-by-step 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:

$P(pink |\ female) = \frac{n(pink\ \&\ female)}{n(female)}$

$P(pink |\ female) = \frac{72}{48+72}$

$P(pink |\ female) = \frac{72}{120}$

$P(pink |\ female) = 0.6$

Next, calculate $P(pink)$

$P(pink) = \frac{n(pink)}{n(Total)}$

$P(pink) = \frac{156 + 72}{156 + 72 + 104 + 48}$

$P(pink) = \frac{228}{380}$

$P(pink) = 0.6$

So, we have:

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

Hence, they are independent

Answer 2

Answer:

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

Step-by-step explanation:

A