Suppose that vehicles taking a particular freeway exit can turn right (R), turn

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.

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

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

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

d. List all outcomes in the even D that exactly two vehicles go in the same direction.

e. List outcomes in D' , C u D, and C n D.

Explanation / Answer

using R,L,S

(a) A={(R,R,R),(L,L,L),(S,S,S)}

(b)B={R,L,S),(R,S,L),(L,R,S),(L,S,R),(S,L,R),(S,R,L)}

(c)C={(L,R,R),(R,L,R),(R,R,L)}

(d)D={(L,L,R),(L,L,S),(R,R,L),(R,R,S),(S,S,L),(S,S,R), (L,R,L),(L,,S,L),(R,L,R),(R,S,R),(S,L,S),(S,R,S),

(R,L,L),(,S,L,L),(L,R,R),(S,R,R),(L,S,S),(R,S,S,) }

(e) CuD={(L,L,R),(L,L,S),(R,R,L),(R,R,S),(S,S,L),(S,S,R), (L,R,L),(L,,S,L),(R,L,R),(R,S,R),(S,L,S),(S,R,S),

(R,L,L),(,S,L,L),(L,R,R),(S,R,R),(L,S,S),(R,S,S,) }

CnD={(L,R,R),(R,L,R),(R,R,L)}

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