Question

What is the probability of getting a sum 10, when two dice are thrown simultaneously?
A.$\dfrac{1}{{12}}$
B.$\dfrac{1}{6}$
C.$\dfrac{1}{9}$
D.$\dfrac{1}{8}$

Answer 1

Hint: We will use the definition of probability to solve the question and then we will calculate the possible outcomes. The total outcomes will be calculated by the formula ${6}^{n}$ where n is the total number of dice thrown. Then using the definition, we will find the probability as:
Probability of an event = the total number of possible outcomes/ the total number of outcomes

Complete step-by-step answer:
We are given that two dice are thrown. We need to find the probability of getting a sum 10 on the dice.
The probability is defined as the likeliness of an event to occur. It is defined as the total number of possible outcomes divided by the total number of events.
We will first find the total number of outcomes using the formula: ${6}^{n}$ where n is the total number of dice. Here, n = 2.
Therefore, the total possible outcomes are: ${6}^{2}$ = 36
Let us list all the possible outcomes as:
{(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)}
Now, we will find out all the possible outcomes who contribute as a sum 10.
Total possible outcomes will be: {(4, 6), (5, 5), (6, 4)}
Therefore, by definition of the probability, we can say
The probability of getting the sum 10 = $\dfrac{the\, total\, number\, of\, possible\, outcomes}{ the\, total\, number\, of\, outcomes}$ = $\dfrac{3}{{36}} = \dfrac{1}{{12}}$
Therefore, option(A) is correct.

Note: In such questions, you will not find difficulty except while constituting the possible outcomes. It is better if you write all the outcomes and then select the required outcomes. Else, it will become a bit more confusing. And, always check that the probability obtained must lie between 0 and 1. Here as well, the probability is 0.0833 which is between 0 and 1.