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. All outcomes in the event A that all three vehicles go in the same direction are All outcomes in the event B that all three vehicles take different directions are All outcomes in the event C that exactly two of the three vehicles turn right All outcomes in the even D that exactly two vehicles go in the same direction

Explanation / Answer

a)

Taking the same direction,

RRR, LLL, SSS

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b)

Permuting SLR (different directions),

RSL, RLS, LRS, LSR, SLR, SRL [ANSWER]

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c)

If 2 go to the right,

RRL, RLR, LRR, RRS, RSR, SRR [ANSWER]

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d)

Hence either 2 go R, or 2 go L, or 2 go S:

RRL, RLR, LRR, RRS, RSR, SRR, LLR, LRL, RLL, LLS, LSL, SLL, SSR, SRS, RSS, SSL, SLS, LSS [ANSWER]

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