Question

You love Cheetos and Frito-Lay is giving away a free bag of Cheetos every week for a year if you collect a Chester Cheetah token, a cheese token and fire token. According to Frito Lay, 80% of bags have a cheese token, 15% have a fire token and 5% have a Chester Cheetah token. Conduct a simulation to determine the number of bags of Cheetos you must purchase to win your free Cheetos for a year. Conduct two trials using the random numbers provided.

Trial #1 03242 50692 18977 28370 49873 21901 83622

Trial #2 78695 21402 85525 81183 76520 98012 45983

Answer 1

80% of bags have a cheese token, 15% have a fire token and 5% have a Chester Cheetah token. The probability distribution of the tokens is

Token	Probability
Cheese	0.8
Fire	0.15
Chester Cheetah	0.05

The cumulative probability and the random number intervals are calculated as given below (expressed as %s)

			Random number intervals
Token	Probability	Cumulative probability	From	less than
Cheese	80%	80%	0%	80%
Fire	15%	95%	80%	95%
Chester Cheetah	5%	100%	95%	100%

That is, to simulate the token from each bag of cheetos that you buy, we use the following steps

• pick 2 digits from the list of random number provided.
• The Token corresponding to the random number interval in which the 2 digits lie is the token in the bag of cheetos.
  • For example, the first 2 digits are 03 and 03 lies in the interval 0 to 80 and hence the token in the bag is Cheese

We create the following table for trial #1

Random Digits	Random number interval	Token	Bag #
03	0-80	Cheese	1
24	0-80	Cheese	2
25	0-80	Cheese	3
06	0-80	Cheese	4
92	80-95	Fire	5
18	0-80	Cheese	6
97	95-100	Chester Cheetah	7

We can see that we have bought 7 bags of cheetos before we get all the 3 tokes and hence win your free Cheetos for a year.

Trial #2

Random Digits	Random number interval	Token	Bag #
78	0-80	Cheese	1
69	0-80	Cheese	2
52	0-80	Cheese	3
14	0-80	Cheese	4
02	0-80	Cheese	5
85	80-95	Fire	6
52	0-80	Cheese	7
58	0-80	Cheese	8
11	0-80	Cheese	9
83	80-95	Fire	10
76	0-80	Cheese	11
52	0-80	Cheese	12
09	0-80	Cheese	13
80	80-95	Fire	14
12	0-80	Cheese	15
45	0-80	Cheese	16
98	95-100	Chester Cheetah	17

ans:

Trial #1: the number of bags of Cheetos you must purchase to win your free Cheetos for a year is 7

Trial #2: the number of bags of Cheetos you must purchase to win your free Cheetos for a year is 17