# FINDING PROBABILITY USING A TABLE

## About "Finding probability using a table"

Finding probability using a table :

Recall that a compound event consists of two or more simple events.

To find the probability of a compound event, we have to write a ratio of the number of ways the compound event can happen to the total number of equally likely possible outcomes.

## Finding probability using a table - Example

Example 1 :

Jacob rolls two fair number cubes. Find the probability that the sum of the numbers he rolls is 8.

Solution :

Step 1 :

List out all the possible outcomes when two cubes are rolled. There are 36 possible outcomes in the sample space.

Step 2 :

Create a table where each cell represents the sum on two number cubes.

Then, circle the outcomes that give the sum of 8. Step 3 :

Find the number of outcomes in which the sum is 8.

Number of outcomes in which the sum is 8  =  5

Step 4 :

Find the required probability.

P (for sum 8)  =  5 / 36

Hence, the probability that the sum of the numbers is 8 is 5/36.

Example 2 :

A six faced number cube is rolled twice. What is the probability of getting a difference of 2 ?.

Solution :

Step 1 :

List out all the possible outcomes when two cubes are rolled. There are 36 possible outcomes in the sample space.

Step 2 :

List out  the outcomes where the difference between two numbers is 2. Step 3 :

Find the number of outcomes in which the difference is 2.

Number of outcomes in which the difference is 2  =  8

Step 4 :

Find the required probability.

P (for difference 2)  =  8 / 36

P (for difference 2)  =  2 / 9

Hence, the probability of getting a difference of 2 is 2/9.

Example 3 :

Two dice are thrown simultaneously. Find the probability that the sum of points on the two dice would be 7 or more.

Solution :

If two dice are thrown then, as explained in the last problem, total no. of all possible outcomes is 36.

Now a total of 7 or more i.e. 7 or 8 or 9 or 10 or 11 or 12 can occur only in the following combinations : Thus the no. of favorable outcomes is 21.

Letting A stand for getting a total of 7 points or more, we have

P(A)  =  21 / 36

P(A)  =  7 / 12

Hence, the probability that the sum of points on the two dice would be 7 or more.

After having gone through the stuff given above, we hope that the students would have understood "Finding probability using a table".

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