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
