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

b. No

Explanation:

Represent

• Square Pizza with S

• Soft Drink with D

Such that

`P(S) = 49\%`

`P(D) = 71\%`

`P(S\ and\ D) = 38\%`

Required

Determine if events S and D are independent

Two events S and D are independent if:

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

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

`P(S\ and\ D) = 49\% * 71\%`

Convert to decimals

`P(S\ and\ D) = 0.49 * 0.71`

`P(S\ and\ D) = 0.3479`

Convert to percentage

`P(S\ and\ D) = 0.3479 * 100\%`

`P(S\ and\ D) = 34.79\%`

The calculated P(S and D) is not equal to 38%

Hence, the events are not independent.