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 315 267 242 131 Order Not Accurate 31 50 33 15 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?

Answer 1

Total = 315 + 267 + 242 + 131 + 31 + 50 + 33 + 15 = 1084

a) With replacement:

Number of orders from D = 131 + 15 = 146

P(Both are from Restaurant D)

= (146/1084)*(146/1084)

= 0.0181 [Rounded off to 4 decimal places]

Yes, the events are independent.

b) Without replacement:

P(Both are from Restaurant D)

= (146/1084)*(145/1083)

= 0.0180 [Rounded off to 4 decimal places]

No, the events are not independent.