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, and what probability would you assign to each one?

b. What is the probability that Cis ranked first?

c. What is the probability that Cis ranked first and Dis ranked last?

Short answer

a. The simple events are\(\left\{ {\left( {CDP} \right),\left( {CPD} \right),\left( {PCD} \right),\left( {DPC} \right),\left( {DCP} \right),\left( {PDC} \right)} \right\}\). The probability of each event is\(\frac{1}{6}\).

b.The probability that C is ranked first is 0.33.

c.The probability that C is ranked first and D is ranked last is 0.167

Step-by-step solution

Given information

The number of cola glasses are 3; labelled as C, D, and P.

The glasses are ordered according to the preferences of an individual.

The same cola has been put into all three glasses.

State the simple events and compute the probability

a.

As there are three different glasses of cola, labelled as C,D, and P.

The simple events for the provided scenario are,

\(\left\{ {\left( {CDP} \right),\left( {CPD} \right),\left( {PCD} \right),\left( {DPC} \right),\left( {DCP} \right),\left( {PDC} \right)} \right\}\)

The total number of outcomes is 6.

Assuming that they all have the same probability of occurrence.

Therefore, the probability of occurrence of any event is \(\frac{1}{6}\).

Compute the probability of C ranked first

b.

The outcomes where C is ranked first are \(\left\{ {\left( {CDP} \right),\left( {CPD} \right)} \right\}\).

The total number of possible outcomes is 2.

The probability that C is ranked first is computed as,

\(\begin{aligned}P\left( {{\rm{C}}\;{\rm{is}}\;{\rm{first}}} \right) &= \frac{{No.\;of\;possible\;outcomes}}{{Total\;number\;of\;outcomes}}\\ &= \frac{2}{6}\\ &= 0.33\end{aligned}\)

Therefore, the probability that C is ranked first is 0.33.

Compute the probability of C ranked first and D ranked last

c.

The outcomes where C is ranked first and D is ranked last are \(\left\{ {\left( {CPD} \right)} \right\}\).

The total number of possible outcomes is 1.

The probability that C is ranked first and D is ranked last is computed as,

\(\begin{aligned}P\left( {{\rm{C}}\;{\rm{is}}\;{\rm{first}}\;{\rm{and}}\;{\rm{D}}\;{\rm{is}}\;{\rm{last}}} \right) &= \frac{{No.\;of\;possible\;outcomes}}{{Total\;number\;of\;outcomes}}\\ &= \frac{1}{6}\\ &= 0.167\end{aligned}\)

Therefore, the probability that C is ranked first and D is ranked last is 0.167.