**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.

**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.

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