Suggested languages for you:

Americas

Europe

Problem 1

# A pair of dice is rolled, and the number that appears uppermost on each die is observed.refer to this experiment and find the probability of the given event. The sum of the numbers is an even number.

Expert verified
The probability of the sum of the numbers being an even number when rolling a pair of dice is $$\frac{1}{2}$$.
See the step by step solution

## Step 1: Listing out possible outcomes

List out all possible outcomes of rolling two dice. There are 36 outcomes as there are 6 sides of each die.

## Step 2: Identifying pairs with even sum

Identify and list out the pairs where the sum of the numbers is an even number. These are the favorable outcomes.

## Step 3: Counting favorable outcomes

Count the number of pairs identified in Step 2. Let this count be represented by x.

## Step 4: Calculating the probability

Calculate the probability of obtaining an even sum by dividing the number of favorable outcomes (x) by the total number of outcomes (36). The probability of obtaining an even sum is given by: $P(Even\,sum) = \frac{x}{36}$ Now, let's put this plan into action.

## Step 1

Listing all the possible outcomes, we get a 6x6 grid (since there are 6 sides on each die): (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

## Step 2

We can find the pairs with an even sum: (1,1) (1,3) (1,5) (2,2) (2,4) (2,6) (3,1) (3,3) (3,5) (4,2) (4,4) (4,6) (5,1) (5,3) (5,5) (6,2) (6,4) (6,6)

## Step 3

Counting the pairs listed above, we have x = 18 favorable outcomes.

## Step 4

Calculating the probability of obtaining an even sum: $P(Even\,sum) = \frac{x}{36} = \frac{18}{36} = \frac{1}{2}$ Therefore, the probability of the sum of the numbers being an even number when rolling a pair of dice is $$\frac{1}{2}$$.

We value your feedback to improve our textbook solutions.

## Access millions of textbook solutions in one place

• Access over 3 million high quality textbook solutions
• Access our popular flashcard, quiz, mock-exam and notes features

## Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

• Flashcards & Quizzes
• AI Study Assistant
• Smart Note-Taking
• Mock-Exams
• Study Planner