Question

Suppose that Mork and Mindy are walking together and reach a crossroad. Each one can turn right (R), turn left (L), or go straight (S). Consider observing the direction they choose. Assume that Mork is walking slightly in front of Mindy and makes his decision ?rst.
a. List all outcomes in the event B that both people go in the same direction. b. List all outcomes in the event C that at least one of the two turns left. c. List all outcomes in the event D that both people take di?erent directions. d. List outcomes in D', C ?B, and C ?D

Answer 1

We use the following notation, the first letter denotes the direction Mork chooses and the second letter denotes the direction Mindy chooses. For example, LS denotes the event that Mork goes right and Mindy goes straight.

(a)

Clearly, B = event that both Mork and Mindy go in the same direction = {RR, LL, SS}

(b)

Let us first enumerate the cases in which Mork goes left : LR, LL, LS

now, we enumerate the cases in which Mindy goes left : RL, LL,SL

Now, the event that atleast one of the two goes left :

C = {LR, LS, LL, RL, SL}

(c)

The sample space of all the possible outcomes, S is given by :

S = {RR, RL, RS, LR, LL, LS, SR, SL, SS}

Now, in the above set we note that Mork and Mindy go different directions in all cases except RR, LL and SS.

Thus, the event that both people take different directions is given by :

D = {RL, RS, LR, LS, SR, SL}

(d)

To find D', we look at the elements which are in S but not in D. These are RR, LL and SS.

Thus, D' = {RR, LL, SS}

We notice that {RR, LL, SS} = B.

Thus, D' = {RR, LL, SS} = B

Now,

C B = {LR, LS, LL, RL, SL} {RR, LL, SS} = {LL}

Also,

C D = {LR, LS, LL, RL, SL} {LR, LS, RL, SL, SR, RS} = {LR, LS, LL, RL, SL, SR, RS}

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