Question

Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles. (Enter your answers in set notation. Enter EMPTY or ∅ for the empty set.)

(a) List all outcomes in the event A that all three vehicles go in the same direction.
A =  

  

(b) List all outcomes in the event B that all three vehicles take different directions.
B =  

  

(c) List all outcomes in the event C that exactly two of the three vehicles turn right.
C =  

  

(d) List all outcomes in the event D that exactly two vehicles go in the same direction.
D =  

  

(e) List outcomes in D'.
D' =  

  

List outcomes in C ∪ D.
C ∪ D =  

  

List outcomes in C ∩ D.
C ∩ D =  

  

Answer 1

Answer:

Given Data,

Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles.

(a).List all outcomes in the event A that all three vehicles go in the same direction:

All the outcomes in the event that all 3 vehicles go in the same direction can be obtained as:

A = { RRR, LLL, SSS }

(b).List all outcomes in the event B that all three vehicles take different directions:

All the outcomes where all the vehicles takes different directions can be obtained as:

B = { RLS, RSL, LSR, LRS, SLR, SRL }

(c).List all outcomes in the event C that exactly two of the three vehicles turn right:

All the outcomes where exactly two of the three vehicles turn right is given as:

C = { RRL, RRS, LRR, SRR, RSR, RLR }

(d). List all outcomes in the event D exactly two vehicles go in the same direction:

All the outcomes where exactly 2 of the three vehicles go in the same direction is given as:

D = { RRL, RRS, LRR, SRR, RSR, RLR, LLR, LLS, RLL, SLL, LSL, LRL, SSL, SSR, LSS, RSS, SRS, SLS }

(e).List outcomes in D^|:

All the outcomes in D' are given as:

D' = { RLS, RSL, LSR, LRS, SLR, SRL, RRR, LLL, SSS }

(f).List outcomes in C D:

All the outcomes here are obtained as:

C D = { RRL, RRS, LRR, SRR, RSR, RLR, LLR, LLS, RLL, SLL, LSL, LRL, SSL, SSR, LSS, RSS, SRS, SLS }

C D = D

(g) List outcomes in C D :

All the outcomes in C \cap D could be represented as:

C D = C = { RRL, RRS, LRR, SRR, RSR, RLR }