Question

Asked Feb 25, 2019

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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.)

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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*) = 6^{2} = 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 ...*

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