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 ABCDOrder Accurate333267249149Order Not Accurate32523619 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?

Answered: are selected, find the probability…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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	333	267	249	149
Order Not Accurate	32	52	36	19

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?

Expert Solution

Step 1

Given:

Total no of orders = Accurate orders + Not accurate orders = 333+267+249+149+32+52+36+19=1137
Total orders from D = Accurate orders of D + Not accurate orders of D = 149+19=168

If two orders are randomly selected with replacement, the probability that they are both from Restaurant D is calculated as:

$P r o b a b i l i t y = P (F i r s t o r d e r f r o m D) \times P (2 n d o r d e r f r o m D) = \frac{168}{1137} \times \frac{168}{1137} = 0.02183$
The events can be considered as independent events because selecting the first order does not affect the probability of the selecting second order.

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