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

Answer:

No

Step-by-step 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 $\ne$

$0.38\ \ne 0.3479$

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