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Question

Answers

A.$\dfrac{1}{{12}}$

B.$\dfrac{1}{6}$

C.$\dfrac{1}{9}$

D.$\dfrac{1}{8}$

Answer
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Probability of an event = the total number of possible outcomes/ the total number of outcomes

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 = $\dfrac{the\, total\, number\, of\, possible\, outcomes}{ the\, total\, number\, of\, outcomes}$ = $\dfrac{3}{{36}} = \dfrac{1}{{12}}$