Question

On throwing two dice, what are the chances of getting a total of 3 or 5 or 11.
A. 5/36
B. 1/9
C. 2/9
D. 19/36

Answer 1

Hint: In case of questions involving dice, it is easier to solve them by writing down all the pairs. On writing down all the pairs formed when one throws two dice, you can get a fair idea of how to proceed further in calculating the total number of chances of getting the required sum, difference, product, quotient, remainder, etc.

Complete step by step solution: 
Let us write down all the pairs we’ll be getting on throwing two dice:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Total number of pairs formed = 36
Now,
All the pairs having a sum of 3 are:
(1,2), (2,1)
All the pairs having a sum of 5 are:
(1,4), (2,3), (3,2) (4,1)
All the pairs having a sum of 11 are:
(5,6), (6,5)
Total number of pairs having a sum of 3 or 5 or 11 = 8
Probability of an event = Total number of favorable outcomes/ Total number of possible outcomes
For calculating the total number of chances of getting a total of 3 or 5 or 11 on throwing two dice, we will have to calculate their probability
Thus,
Total number of favorable outcomes = Total number of pairs having a sum of 3 or 5 or 11 = 8
Total number of possible outcomes = Total number of pairs formed = 36
Hence,
Probability of getting a total of 3 or 5 or 11 on throwing two dice $ = \dfrac{8}{{36}}$
On simplifying further,
The total number of chances of getting a total of 3 or 5 or 11 $ = \dfrac{2}{9}$
Therefore, the correct option is C.

Note: Keep in mind to include all the required pairs and if the question is asking for “AND” or “OR”. Students often get confused with these two keywords, in particular. In case of “OR” you add the probabilities and in case of “AND” you multiply them instead.