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 326 260 238 134 Order Not Accurate 33 55 38 18 If two orders are​ selected, find the probability that they are both accurate. Complete parts​ (a) and​ (b) below. a. Assume that the selections are made with replacement. Are the events​ independent? The probability is nothing. The events ▼ are not are independent. ​(Round to three decimal places as​ needed.) b. Assume that the selections are made without replacement. Are the events​ independent? The probability is nothing. The events ▼ are not are independent. ​(Round to three decimal places as​ needed.)

Answer 1

	A	B	C	D	Total
Not Accurate	326	260	238	134	958
Accurate	33	55	38	18	144
Total	359	315	276	152	1102

(a) Total number of accurate orders = 144

P(That the first order is accurate) = 144/1102

P(The second order is also accurate, after replacement) = 958/1102

Therefore the required probability = (144/1102) * (144/1102) = 0.017

YES the events are independent, as the probability of the first event does not depend on the probability of the second.

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(b) P(That the first order is accurate) = 144/1102

P(The second order is also accurate, without replacement) = 143/1101

Therefore the required probability = (144/1102) * (143/1101) = 0.017

NO, the events are not independent, as the probability of the first event depends on the probability of the second.