Asked Feb 25, 2019

For the experiment of rolling an ordinary pair of dice, find the probability that the sum will be odd or a multiple of 5. (You may want to use a table showing the sum for each of the 36 equally likely  outcomes.)


Expert Answer

1 Rating
Step 1

Concept of probability:

Probability deals with the likelihood of occurrence of a given event. The probability value lies between 0 and 1. An event with probability 1 is considered as certain event and an event with probability 0 is considered as an impossible event. The probability of 0.5 infers of having equal odds of occurring and not occurring of an event.

The general formula to obtain probability of an event A is,

P(A) = (number of favorable elements for event A)/(Total number of elements in the sample space).

The basic properties of probability are given below:

Step 2

Find the sample space:

Sample space:

The set of all possible outcomes of a probability experiment is called sample space of the experiment.

Here, two fair dice are rolled.

The total number of outcomes in the sample space be n(S) = 62 = 36. That is, there will be 36 equally likely outcomes.

Outcomes will be occurred in ordered pairs. First number in each ordered pair represents the number on the first die and second number in each ordered pair represents the number on the second die. Each of the two numbers can take values 1 to 6.

The sum of the numbers on the dice will be 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.

The sample space for the experiment is given below:

Step 3

Find the outcomes that match the desired requirement:

Here, the requirement is the sum of the numbers on the pair of rolled die should be odd or a multiple of 5.

Consider that an event A denotes that sum of the dice is odd and an event B denotes the sum of the dice is a multiple of 5.

The outcomes in favor of the event A:

Event A is the sum of the dice is odd. For the sum of the dice to be odd, the sum must be any of 3, 5, 7, 9 and 11.

The outcomes in the event A consist of all the possible outcomes for the sum of the dice to be 3, 5, 7, 9 and 11.

The outcomes in favor of the event A are:

A = {(1,2), (2,1), (1,4), (2,3), (3,2), (4,1), (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), (3,6), (4,5),(5,4), (6,3), (5,6), (6,5)}.

The outcomes in favor of the ...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in



Related Probability Q&A

Find answers to questions asked by student like you
Show more Q&A

Q: Let A = {4, 6}, B = {6, 11, 23}, D = {35} and S = sample space = A ∪ B ∪ D. Identify Ac ∩ B.a) {4, ...

A: Given information:The given events are as follows:A = { 4, 6 }, B = { 6, 11, 23 }, D = { 35 } and th...


Q: Quick Start Company makes 12-volt car batteries. After many years of product testing, the company kn...

A: If a random variable x has a distribution with mean µ and standard deviation σ, then the z-score is ...


Q: Use the Alternative formula for Variance to calculate the variance of the random variable in Table 1...

A: Find the mean of the random variable k using the given probability distribution.Discrete random vari...


Q: What is the chromatically number of this graph? Find a coloring of the graph using that many colors....

A: Given a graph as shown below.The Chromatic number of any graph is the smallest number of colors need...


Q: When two dice are tossed, find the odds in favor of getting a sum of 7.

A: Odds in favor:Odds in favor of a particular event are the ratio of number of favorable outcomes of t...


Q: A company is in the business of finding addresses of long-lost friends. The company claims to have a...

A: The distribution:The company claims to have 80% success rate. There are names of six friends for who...


Q: x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal...

A: According to the given question, x be a random variable representing dividend yield of bank stocks. ...


Q: How many diffrent four -letter strings can be formed from the letters A,B,C,D,E(repeats allowed) if ...

A: The given letters are  A,B,C,D,E. Out of them B,C,D are consonant, A and E are vowel.The first three...


Q: For this problem, carry at least four digits after the decimal in your calculations. Answers may var...

A: In this question, we need to find the sample size for the proportion of females when no preliminary ...