Probability

Concept: When two fair dice are rolled, each die has

6

possible outcomes. Therefore, the total number of possible outcomes is:

6%20%5Ctimes%206%20%3D%2036

Each outcome is equally likely.
Step 1: List all outcomes whose sum is

9

.
The pairs of numbers whose sum equals

9

are:

(3%2C6)%2C%20(4%2C5)%2C%20(5%2C4)%2C%20(6%2C3)

Thus, the number of favorable outcomes is:

4

Step 2: Apply the probability formula.
The probability of an event is given by:

P(E)%20%3D%20%5Cfrac%7B%5Ctext%7BNumber%20of%20favorable%20outcomes%7D%7D%7B%5Ctext%7BTotal%20number%20of%20possible%20outcomes%7D%7D

Substituting the values:

P(%5Ctext%7Bsum%20%7D%20%3D%209)%20%3D%20%5Cfrac%7B4%7D%7B36%7D

Step 3: Simplify the fraction.

%5Cfrac%7B4%7D%7B36%7D%20%3D%20%5Cfrac%7B1%7D%7B9%7D

Step 4: Conclusion.
Therefore, the probability of obtaining a sum of

9

when two fair dice are rolled is:

%5Cfrac%7B1%7D%7B9%7D

Chapter Questions
1 MCQs