please explain and show work 1 Any car arriving at a certain

please explain and show work

1. Any car arriving at a certain intersection can either turn left, turn right, or continue straight ahead, An experiment consists of observing the movement of two cars intersection. at this (a) List all the outcomes in the sample space (b) Find the probability that at least one car continues straight ahead (c) Find the probability that both cars go in the same direction.

Solution

a).

L= left, R= Right and S= straight

For car1 three possibilities ( L1, R1, S1)

For car2 three possibilities ( L2, R2, S2)

The sample space = (L1L2,L1R2,L1S2,R1L2,R1R2,R1S2,S1L2,S1R2,S1S2)

WHERE L1L2 means both car1 and car2 turns left.

b)

total sample points =9

at least one car drives straight =( L1S2 ,R1S2,S1L2,S1R2,S1S2)

P( at least one car drives straight) =5/9 =0.5556

C).

Both in the same direction = (L1L2, R1R2,S1S2)

P(Both in the same direction ) = 3/9 =0.3333