91Ó°ÊÓ

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.

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 \(\frac{1}{6}\).

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.

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.