An individual is presented with three different glasses of cola, labeled C, D, and P. He is asked to taste all three and then list them in order of preference. Suppose the same cola has actually been put into all three glasses.a. What are the simple events in this ranking experiment, and what probability would you assign to each one?b. What is the probability that C is ranked first?c. What is the probability that C is ranked first and D is ranked last?

Question
Asked Sep 8, 2019

An individual is presented with three different glasses of cola, labeled C, D, and P. He is asked to taste all three and then list them in order of preference. Suppose the same cola has actually been put into all three glasses.

a. What are the simple events in this ranking experiment, and what probability would you assign to each one?

b. What is the probability that C is ranked first?

c. What is the probability that C is ranked first and D is ranked last?

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Expert Answer

Step 1

a. The simple events in this ranking experiment are {CDP, CPD, DCP, DPC, PCD, PDC}.

The probability assign to the first event is obtained as follows:

Probability Number of times first event occurs
Total number of events
1
6
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Probability Number of times first event occurs Total number of events 1 6

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Step 2

This probability is same for all the six events. Thus, the probability assign to each event is 1/6.

Step 3

b. From the simple events it can be seen that simple events that C rank first is CDP and CPD. That is, the number of events that C ra...

Number of events as C rank first
Total number of events
P(C rank first)
2
6
1
3
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Number of events as C rank first Total number of events P(C rank first) 2 6 1 3

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