Use the data in the following table, which lists drive-thru order accuracy at po

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.
Restaurant A   Restaurant B   Restaurant C   Restaurant D
Order Accurate   322   268   230   142
Order Not Accurate   39   57   35   11

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?

Explanation / Answer

The sum of all oders is 322 + 268 + 230 + 142 + 39 + 57 + 35 + 11 = 1104.

The probability that an order is from Restaurant D = 11/1104

=> Probability that both orders are from Restaurant D = 11C2 / 1104C2 = 55 / 608856

= 0.00009

a. If the selections are made with replacement, the second order does not depend on the first. The events are independent.

b. If the selections are made without replacement, the second order depends on the first. The events are not independent.

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