Question

What is the probability of getting an odd number if you throw a 6-sided dice? A. 5/6 B. 2/3 C. 1/3 D. 1/2 E. 1/6

Short answer

D. 1/2

Step-by-step solution

- Identify possible outcomes

List all possible outcomes when you throw a 6-sided dice: 1, 2, 3, 4, 5, 6.

- Identify favorable outcomes

Pick out the odd numbers from the list of possible outcomes: 1, 3, 5.

- Count favorable outcomes

Count how many odd numbers are in the list: There are 3 odd numbers (1, 3, and 5).

- Count total possible outcomes

Count the total number of outcomes on a 6-sided dice: There are 6 possible outcomes.

- Calculate the probability

The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. So, the probability is \(\frac{3}{6} = \frac{1}{2}\).

– Choose the correct answer

Compare the calculated probability to the given answer choices. The correct choice is D. \(\frac{1}{2}\).

Key concepts

Probability

Probability is the measure of how likely an event is to occur. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this example, the event is rolling an odd number on a 6-sided dice. The formula for probability is given by:
\[\text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} \]
In the case of the 6-sided dice, there are 6 possible outcomes (1, 2, 3, 4, 5, 6), and 3 of these are odd numbers (1, 3, 5). So, the probability of rolling an odd number is \[\frac{3}{6} = \frac{1}{2}\]
This means that there is a 50% chance of rolling an odd number on a 6-sided dice.

GMAT Preparation

Preparing for the GMAT involves mastering various types of questions, including probability problems. These questions test your ability to apply mathematical concepts to real-world scenarios. Here are some tips for preparing for probability questions:

• Understand the basic principles of probability, including outcomes and events.
• Practice identifying favorable outcomes and calculating probabilities using different types of dice or card decks.
• Review and practice problems from previous GMAT exams to get a feel for the types of probability questions you might encounter.

This exercise on rolling a 6-sided dice and calculating the probability of getting an odd number is a great example of a basic probability problem you might see on the GMAT.

Dice Outcomes

A 6-sided dice (also known as a die) has six faces, each showing a different number ranging from 1 to 6. Each face of the dice represents a possible outcome when it is rolled. Here are the key points regarding dice outcomes:

• When rolling a fair 6-sided dice, each outcome (1, 2, 3, 4, 5, 6) is equally likely.
• There are specific outcomes based on different types of dice; for example, an 8-sided dice would have outcomes ranging from 1 to 8.

For this exercise, the possible outcomes are 1, 2, 3, 4, 5, and 6. By focusing on the odd numbers (1, 3, 5), we are identifying the favorable outcomes needed to calculate the probability.

Mathematical Reasoning

Mathematical reasoning involves logically thinking through a problem to find a solution. For probability questions like the one in this exercise, it encompasses:

• Identifying all possible outcomes.
• Determining the favorable outcomes.
• Using fractions to calculate probabilities.

The steps to solve the problem are:

• Listing all possible outcomes on a 6-sided dice: {1, 2, 3, 4, 5, 6}
• Identifying the favorable outcomes (odd numbers): {1, 3, 5}
• Counting the favorable outcomes: 3 outcomes
• Counting total outcomes: 6 outcomes
• Calculating the probability: \[\frac{3}{6} = \frac{1}{2}\]

Mathematical reasoning ensures each step is logically coherent and leads to the correct conclusion. Practice developing this logical flow to improve performance on similar problems.