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 316 260 246 122 Order Not Accurate 39 55 36 20 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 nothing. The events ? are not are independent because choosing the first order ? affects does not affect the choice of the second order.

Answer 1

No. of orders from restaurant D = 122 + 20 = 142.
Total no. of orders = 316 + 260 + 246 + 122 + 39 + 55 + 36 + 20 = 1094.

(a) Prob. (with replacement) = (142/1094) * (142/1094) = 0.0168.
The events are independent because choosing the first order does not affect the choice of the second order.

(b) Prob. (with replacement) = (142/1094) * (141/1093) = 0.0167.
The events are not independent because choosing the first order affects the choice of the second order.