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.)
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.
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