Question

Suppose 49 percent of the customers at Pizza Palooza order a square pizza, 71 percent order a soft drink, and 38 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza?

a. Yes
b. No

Answer 1

No

Explanation:

Given

`Square\ Pizza = 49\%`

`Soft\ Drink= 71\%`

Required

Are both events independent?

Let P(S) be the probability that a customer orders a square pizza.

`P(S) = 49\%`

Convert to decimal

`P(S) = 0.49`

Let P(D) be the probability that a customer orders a soft drink.

`P(D) = 71\%`

Convert to decimal

`P(D) = 0.71`

From the question, we have that:

`P(S\ and\ D) = 0.38`

For events S and D to be independent:

The following condition must be true

`P(S\ and\ D) = P(S) * P(D)`

Substitute values for P(S and D), P(S) and P(D)

`0.38\ [\ \ ] 0.49 * 0.71`

`0.38\ [\ \ ] 0.3479`

Complete the blank with
`\\e`

`0.38\ \\e 0.3479`

Since both sides are not equal, then the events are not independent.