Question

A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the3 cars each time that passenger rides the roller coaster. If a certain passenger is to ridethe roller coaster 3 times, what is the probability that the passenger will ride in each ofthe 3 cars?

Answer 1

The probability is 0.2222

Step-by-step explanation:

By the rule of multiplication, we know that there are 27 ways to ride the roller coaster 3 times. This is calculated as:

3 * 3 * 3 = 27

1st ride 2nd ride 3rd ride

Because there are 3 cars for the first ride, 3 cars for the second ride and 3 cars for the third ride.

On the other hand, there are 6 ways to ride the roller coaster 3 times and ride in each of the 3 cars. This is calculated as:

3 * 2 * 1 = 6

1st ride 2nd ride 3rd ride

Because, on the first ride, the passenger can choose any of the 3 cars, then for the second ride he can choose any of the 2 cars that he doesn't choose on the first ride and for the third ride he can choose 1 car.

Finally, the probability is calculated as a division of:

`P=(6)/(27)= 0.2222`