Question: A coin has two sides. One side has the number 1 on it and the other side has the number on it. If the coin is flipped three times, what is the probability that the sum of the numbers on the landing side of the coin will be greater than 4?

1. \(\frac{3}{8}\)
2. \(\frac{1}{16}\)
3. \(\frac{1}{8}\)
4. \(\frac{1}{2}\)
5. \(\frac{1}{4}\)

Answer:
Solution eith Explanation: 
Approach Solution (1):

Cases for the sum to be greater than 4 are as mentioned below:

Case 1: (1, 2, 2)
Case 2: (2, 1, 2)
Case 3: (2, 2, 1)
Case 4: (2, 2, 2)
Total outcomes: 2 * 2 * 2 = 8
Probability = Favorable outcomes / Total Outcomes
Therefore, Probability = 4/8 = ½

Correct Option: D

Approach Solution (2):

Drawing the probability tree, first throw 1 or 2 will come, 2nd throw 1 or 2 will come, 3rd throw 1 or 2 will come. Therefore, there are only 4 ways out of 8 for which sum of the numbers will be greater than 4.

Cases:
1-2-2
2-1-22-2-1
2-2-2

Hence probability = 4/8 = 1/2

Correct Option: D

Approach Solution (3):

The number of the total outcomes and outcomes that give us what we want are relatively low, so calculating the answer to the given question isn’t too difficult or time-consuming. In these types of prompts, it’s sometimes faster to calculate what we “don’t want” and then subtract that from 1 (to determine the probability of what we do want).

Here, there are two outcomes that will not match what we are looking for: a sum or 3 or a sum of 4.

Ways to get a sum of 3:
1-1-1

Ways to get a sum of 4:
1-1-2
1-2-1
2-1-1

Each coin has two possible outcomes, so there are 2 * 2 * 2 = 8 possible permutations
4/8 = probability of what we don’t want
1 – 4/8 = probability of what we do want
1 – 4/8 = 4/8 = 1/2

Correct Option: D

“A coin has two sides. One side has the number 1 on it and the other side has the number on it. If the coin is flipped three times, what is the probability that the sum of the numbers on the landing side of the coin will be greater than 4?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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