Question

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? (Enter your answers as a comma-separated list.

( )

What probability would you assign to each one?

A. It is impossible to determine the probability of the simple events with the given information.

B. The probability of an individual event where D is ranked first is 1/12. The probability of another individual event is1/4.

C. The probability of an individual event where D is ranked first is 1/5.The probability of another individual event is

1/15.

D. All of the simple events have the same probability, 1/6.

E. All of the simple events have the same probability, 1/3.

(b) What is the probability that C is ranked first? (Round your answer to three decimal places.)

(c) What is the probability that C is ranked first and D is ranked last? (Round your answer to three decimal places.)

Answer 1

Question:

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? (Enter your answers as a comma-separated list.

What probability would you assign to each one?

(b) What is the probability that C is ranked first? (Round your answer to three decimal places.)

(c) What is the probability that C is ranked first and D is ranked last? (Round your answer to three decimal places.)

Answer:

(a)

Sample Space= {CDP, CPD,DCP,DPC,PCD,PDC}

Probability of each = 1/6

(b)

Probability of C ranking first = 0.333

(c)

Probability of C ranking first and D ranking last = 0.167

Step-by-step explanation:

Let C = Cup 1

Let D = Cup 2

Let P = Cup 3

(a) The possible events

Let SS = Sample Space = The possible outcomes

The possible outcomes are

CDP

CPD

DCP

DPC

PCD

PDC

So, SS = {CDP, CPD,DCP,DPC,PCD,PDC}

Possibly outcome = 6

Probability of each event = number of possible outcomes/Number of Total outcomes

Probability of each event = 1/6

(b)

Probability that C is ranked first

Looking at the sample space (SS), you'll notice that only two events starts with C

The events are CDP and CPD

So the probability = 2/6

Probability = 0.333

(c)

Probability that C ranks first and D ranked last.

Looking at the sample space, you'll notice that only one event satisfies the condition

The event is CPD

So, the probability is 1/6

Probability = 0.167