Question

Use the data in the following​ table, which lists​ drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.

​Drive-thru Restaurant

A B C D

Order Accurate 325 275 244   122

Order Not Accurate 35 53   32    11

If two orders are​ selected, find the probability that they are both from Restaurant D.

a. Assume that the selections are made with replacement. Are the events​ independent?

b. Assume that the selections are made without replacement. Are the events​ independent?

a. Assume that the selections are made with replacement. Are the events​ independent?

The probability of getting two orders from Restaurant D is ?. The events ▼ are/ are not independent because choosing the first order ▼ affects/ does not affect the choice of the second order. ​(Round to four decimal places as​ needed.)

Answer 1

a.

Number of orders from Restaurant D = 122 + 11 = 133

Total number of Orders = 325 + 275 + 244 + 122 + 35 + 53 + 32 + 11 = 1097

Probability that they are both from Restaurant D = (133 / 1097) * (133 / 1097) = 0.0147

The events are independent as the orders from Restaurant D will be unchanged in the next selection.

The probability of getting two orders from Restaurant D is 0.0147. The events are independent because choosing the first order does not affect the choice of the second order.​

b.

If the selections are made without replacement, the order will be reduced by 1 in next selection.

Probability that they are both from Restaurant D = (133 / 1097) * (132 / 1096) = 0.0146

The events are not independent as the orders from Restaurant D will be changed in the next selection.

The probability of getting two orders from Restaurant D is 0.0146. The events are not independent because choosing the first order affects the choice of the second order.​