Suppose that vehicles taking a particular freeway exit can t

Suppose that vehicles taking a particular freeway exit can turn right (R). turn left (L). or go straight (S). Consider observing the direction tor each of three successive vehicles. List all outcomes in the event A that all three vehicles go in the same direction. List all outcomes in the event B that all throe vehicles take different directions. List all outcomes in the event C that exactly two of the throe vehicles turn right. List all outcomes in the even D that exactly two vehicles go in the same direction. List outcomes in D\', C union D, and C intersection D.

Solution

a)

If vehicles go in same direction then they can go either in right or left or straight that is outcomes here are three.

A={straight straight straight , right right right , left left left}

b)

in this case first vehicle coming can take three ways that is right ,left or straight and then second vehicle will have only two ways left(that are not choosen by first vehicle) and then third vehicle will have only one way left so possible outcomes are:-

3*2*1=6

B={right left straight , right straight left , left straight right , left right straight , straight left right , straight right left}

c)

for exactly two of the three vehicles to turn right first we have to choose which two vehicles -- 3C2=3

now one that is left can go either straight or left that it means it has 2 options

so, no. of outcomes =3C2*1*2=6

C={right right straight , right right left , straight right right , left right right , right straight right ,   right left right}

d)

for exactly two of the three vehicles to go in same direction first we have to choose which two vehicles -- 3C2=3

now the choosen vehicle has 3 possibilities

now one that is left will have 2 possibilities(left by above choosen vehicles)

so, no. of outcomes =3C2*3*2=18

   D={right right straight , right right left , straight right right , left right right , right straight right ,   right left right , straight straight right , straight straight left , right straight straight  , left straight straight  , straight right straight  , straight left straight  , left left right , left left straight , right left left  , straight left left  , left right left  , left straight left}

e)

D\' means exactly two vehicles do not go in the same direction that means either all three vehicle will go in different direction or all three vehicles will go in same direction

   D\'={right left straight , right straight left , left straight right , left right straight , straight left right , straight right left , right right right  , left left left  , straight straight straight}

(C U D)={right right straight , right right left , straight right right , left right right , right straight right ,   right left right , straight straight right , straight straight left , right straight straight  , left straight straight  , straight right straight  , straight left straight  , left left right , left left straight , right left left  , straight left left  , left right left  , left straight left}

(C intersection D)={right right straight , right right left , straight right right , left right right , right straight right ,   right left right}