McDonald’s Burger King Wend y’s Taco Bell Order Accurate 334 288 243 145 Order N
ID: 3057017 • Letter: M
Question
McDonald’s
Burger King
Wendy’s
Taco Bell
Order Accurate
334
288
243
145
Order Not Accurate
28
30
37
13
Part One (14 points): Basic Concepts of Probability The table below lists drive-thru order accuracy at popular fast food chains (data from a 2016 QSR Drive- Thru Study). Assume that orders are randomly selected from those included in the table. If one order is selected, what is the probability:
1. Of the order being accurate?
2.Of the order not coming from Wendy’s?
3. Of the order being from McDonald’s or not accurate?
4. Of the order being from Burger King and Taco Bell (at the same time)? McDonald’s Burger King Wendy’s Taco Bell Order Accurate 334 288 243 145 Order Not Accurate 28 30 37 13 If two orders are selected, find the probability that:
5. They are both from Taco Bell if the selections are made with replacement. Are the events independent?
6. They are both from Taco Bell if the selections are made without replacement. Are the events independent?
7. One is from McDonald’s and the other is accurate. Are the events disjoint?
Part Two: More Advanced Probability
If one order is selected, find the probability that:
8)The order came from Burger King, given that it was not accurate.
9)The order was not accurate, given that it came from Burger King.
10) In a sentence, explain why the two probabilities from #6 and #7 are not the same.
Part Three: Counting
Quicken Loans offered a prize of $1 billion dollars to anyone who could correctly predict the winner of the NCAA basketball tournament. After the “play-in” games, there are 64 teams in the tournament. The 64 teams play each other in a series of single elimination games until there is 1 championship team.
11)How many distinct team games (not rounds!) are required to get 1 championship team from the field of 64 teams?
12)If you make random guesses for each team game of the tournament, find the probability of picking the winner in every game.
McDonald’s
Burger King
Wendy’s
Taco Bell
Order Accurate
334
288
243
145
Order Not Accurate
28
30
37
13
Explanation / Answer
The summary is in the below table:
1. Total no. of accurate orders = 1010
Total no. of inacurate orders = 108
Probability of a randomlypicked order being accurate = 1010 / (1010+108) = 0.9034
2. Total no. of orders that came from Wendy's = 280.
So orders not coming from Wendy's = 1118 - 280 = 838
So the probability of a randomly chosen order not coming from Wendy's = 838/1118 = 0.7496
3. No. of orders which are from McDonald’s or not accurate = 362 + 108-28 = 442
So the probability of a randomly chosen order being rom McDonald’s or not accurate = 442 / 1118 = 0.3953
4. The the order being from Burger King and Taco Bell = (318+158) / 1118 = 0.4258
5. If two orders are selected with replacement, probability of both being from Taco Bell = (158/1118) x (158/1118) = 0.02.
The events are independent because the outcome of one event doesn't affect the outcome of the other event.
6. If two orders are selected without replacement, probability of both being from Taco Bell = (158/1118) x (157/1117) = 0.0199.
The events are not independent, because the probability of the second event changes depending on the outcome of the 1st event.
7. If two orders are selected, the possible combinations for the event one is from McDonald's and the other is accurate
one order is from McDonald's and is accurate, the other order is any accurate
one order is from McDonald's and is not accurate, the other order is any accurate
the probability that one is from McDonald's and the other is accurate = (334/1118) x (1009/1117) + (28/1118) x (1010/1117) = (334x1009+18x1010) / (1118 x 1117) = 0.2844
McDonald’s Burger King Wendy’s Taco Bell Order Accurate 334 288 243 145 1010 Order Not Accurate 28 30 37 13 108 362 318 280 158 1118