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

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

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Step 1

Odds in favor:

Odds in favor of a particular event are the ratio of number of favorable outcomes of that event to the number of unfavorable outcomes of that event.

Consider an event A.

The odds in favor of the event A are obtained as given below:

Step 2

Find the sample space:

Sample space:

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

Here, two fair dice are rolled.

The total number of outcomes in the sample space is 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, 11 and 12.

The sample space for the experiment is given below:

Step 3

Find the odds in favor of getting a sum of 7:

Here, the requirement is that, the sum of the numbers on the pair of rolled dice should be equal to 7.

The event sum of the dice is equal to 7 is denoted by A.

The outcomes in favor of the event A:

The outcomes in the event A consist of all the possible outcomes for the sum of the dice to be 7.

The outcomes in favor of the event A are:

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

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### Basic Probability 