Question

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

a. List all outcomes in the event A that all three vehicles go inthe same direction.
b. List all outcomes in the event B that all three vehicles takedifferent directions.
c. list all outcomes in the event C that exactly two of the threevehicles turn right.
d. List all outcomes in the event C that exactly two of the threevehicles turn right.
e. List outcomes in D', C U D, and C D

Answer 1

a.) A= [RRR, LLL, SSS]

b.) B=[RLS, RSL, SRL, SLR, LRS, LSR]

c.) C=[RRL, RRS, RSR, RLR, SRR, LRR]

e.) D'= C' = [RRR, LLL, SSS, RLS, RSL, SRL, SLR, LRS, LSR, LLR, LLS, LSL, LRL, SLL, RLL, SSL, SSR, SLS, SRS, RSS, LSS]

Explanation:

If three consecutive vehicles are considered with their direction as R, L and S, then

a.) when the three vehicles go in same direction, A= [RRR, LLL, SSS]

b.) When the three vehicles take the different direction, B=[RLS, RSL, SRL, SLR, LRS, LSR]

c.) when exactly two vehicles turn right, C=[RRL, RRS, RSR, RLR, SRR, LRR]

d.) repeated question of C above.

e.) D'= C' = [RRR, LLL, SSS, RLS, RSL, SRL, SLR, LRS, LSR, LLR, LLS, LSL, LRL, SLL, RLL, SSL, SSR, SLS, SRS, RSS, LSS]