91Ó°ÊÓ

The vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S).

a.

Event A represents that all three vehicles go in the same direction.

The possible outcomes of event A is,

\(A = \left\{ {RRR,LLL,SSS} \right\}\)

b.

Event B represents that all three vehicles take different directions.

The possible outcomes of event B is,

\(B = \left\{ {RSL,RLS,LRS,LSR,SLR,SRL} \right\}\)

c.

Event C represents that; exactly two out of the three vehicles turn right.

The possible outcomes of event C is,

\(C = \left\{ {RRS,RRL,LRR,SRR,RLR,RSR} \right\}\)

d.

Event D represents that exactly two vehicles go in the same direction.

The possible outcomes of event D is,

\(DC = \left\{ {RRS,RRL,LRR,SRR,RLR,RSR,LLS,LLR,RLL,SLL,LRL,SSL,SSR,SRS,SLS,LSS,RSS} \right\}\)

e.

Referring to part c and d,

\(C = \left\{ {RRS,RRL,LRR,SRR,RLR,RSR} \right\}\)

\(D = \left\{ {RRS,RRL,LRR,SRR,RLR,RSR,LLS,LLR,RLL,SLL,LRL,SSL,SSR,SRS,SLS,LSS,RSS} \right\}\)

The complementary of an event D consists of all the outcomes that are not contained in D.

This implies that the event\(D'\)will contain all the outcomes of the vehicles that go in the same direction or in a different direction.

\(D' = \left\{ {RRR,SSS,LLL,RLS,RSL,LSR,LRS,SLR,SRL} \right\}\)

A union of two events C and D consists of all the outcomes that are either in C or D or in both events

\(\begin{aligned}C \cup D &= \left\{ {RRS,RRL,LRR,SRR,RLR,RSR,LLS,LLR,RLL,SLL,LRL,SSL,SSR,SRS,SLS,LSS,RSS} \right\}\\ &= D\end{aligned}\)

The intersection of two events C and D consists of all the outcomes that are present in both events.

\(\begin{aligned}C \cap D &= \left\{ {RRS,RRL,LRR,SRR,RLR,RSR} \right\}\\ &= C\end{aligned}\)