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 336 268 245 124 Order Not Accurate 36 59 38 17 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 are not 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.

Answer 1

The table with the Totals are as below:

	A	B	C	D	Total
Accurate	336	268	245	124	973
Not Accurate	36	59	38	17	150
Total	372	327	283	141	1123

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(a) P(Picking 2 orders with replacement and they are both accurate)

Probability = favourable outcomes/Total Outcomes.

1st Pick: Accurate orders = 973 and Total orders = 1123. Therefore the probability = 973/1123

2nd Pick: Accurate orders = 973 and Total orders = 1123. Therefore the probability = 973/1123

The required probability = (973/1123) * (973/1123) = 0.75069    0.751 (Rounding to 3 decimal places)

Since the probability is done with replacement, the outcome of the first event does not affect the outcome of the second event, and hence the 2 events are independent.

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(b) P(Picking 2 orders without replacement and they are both accurate)

Probability = favourable outcomes/Total Outcomes.

1st Pick: Accurate orders = 973 and Total orders = 1123. Therefore the probability = 973/1123

2nd Pick: Accurate orders = 972 and Total orders = 1122 (SInce we are doing without replacement). Therefore the probability = 972/1122

The required probability = (973/1123) * (972/1122) = 0.75059    0.751 (Rounding to 3 decimal places)

Since the probability is done without replacement, the outcome of the first event will affect the outcome of the second event, and hence the 2 events are not independent.

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