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

1. 0
2. 1/9
3. 2/9
4. 1/3
5. 1

Correct Answer: (C)

Solution and Explanation:
Approach Solution 1:

The problem statement informs that:

Given:

• A certain roller coaster has 3 cars.
• A passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster
• passenger rides the roller coaster 3 times

Find Out:

• The probability that the passenger will ride in each of the 3 cars

A passenger can ride any car the first time: p=1;
The passenger must ride another car the second time: p=2/3;
The passenger must ride not the 2 cars already driven by him the third time: p=1/3.

Therefore, P=1∗ ⅔ ∗ ⅓ =2/9.

Hence, the probability that the passenger will ride in each of the 3 cars = 2/9

Approach Solution 2:

The problem statement states that:

Given:

• A certain roller coaster has 3 cars.
• A passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster
• passenger rides the roller coaster 3 times

Find Out:

• The probability that the passenger will ride in each of the 3 cars

The total number of ways the passenger can drive 3 cars (that is for 3 rides) is 3^3 (since the passenger holds 3 options for each ride);
Therefore, the number of ways the passenger can drive 3 distinct cars is 3! ( that is ABC, ACB, BAC, BCA, CAB, CBA);

Hence, P= 3!/3^3 =2/9

Therefore, the probability that the passenger will ride in each of the 3 cars is 2/9

Approach Solution 3:

The problem statement implies that:

Given:

• A certain roller coaster has 3 cars.
• A passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster
• passenger rides the roller coaster 3 times

Find Out:

• The probability that the passenger will ride in each of the 3 cars

Let’s solve the question by using the reverse probability approach. This is the easiest and quickest way to decipher the problem.

P = 1-q. (where q = probability that the passenger rides only in one or in two cars, but not in the three).
q=1∗ ⅓ ∗1/3 ∗3 + 1∗ ⅓ ∗ ⅓ ∗ 4 =1/9 ∗3 + 1/9 ∗4 = 7/9

The first term is multiplied by 3 since the passenger could use A, B or C.

The second term is multiplied by 4 since the passenger could use A&B, A&C, C&B or B&C.

Therefore, P=1−7/9 = 2/9

Hence, the probability that the passenger will ride in each of the 3 cars is 2/9.

“A certain roller coaster has 3 cars, and a passenger is equally likely''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions are designed to measure the numerical literacy and calculative skills of the candidates to solve mathematical problems. GMAT Quant practice papers provide several types of questions that help to strengthen the calculative knowledge of the candidates.

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