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 |
340340 |
273273 |
246246 |
141141 |
|
Order Not Accurate |
4040 |
6060 |
3939 |
1313 |
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
are not
independent because choosing the first order
▼
does not affect
affects
the choice of the second order.
(Round to four decimal places as needed.)
b. Assume that the selections are made without 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
▼
does not affect
affects
the choice of the second order.
Total orders = 340 + 273 + 246 + 141 + 40 + 60 + 39 + 13 = 1152
Total orders from restaurant D = 141 + 13 = 154
a) The events are not independent because choosing the first order does not affect the choice of the second order.
P(both orders are from restaurant D) = (154 / 1152)2 = 0.0179
b) The events are independent because choosing the first order affects the choice of the second order.
P(both orders are from restaurant D) = (154/1152) * (153/1151) = 0.0178
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