Question

In a simultaneous throw of two dice, what is the probability of getting a total of 11?

Answer 1

Hint: To find the probability of any outcome the formula is as follows: $\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$ . Now, we have simultaneously thrown 2 dice so the total outcomes will be 6 multiplied by 6 because in the two dice throw, each dice can have 6 possibilities so the two dice have 6 multiplied by 6 possibilities. The favorable outcomes are those in which the sum of observations on the two dice is 11 so list those cases in which the sum of the two dice is 11. After that, substitute the values of favorable outcomes and the total outcomes in the probability formula.

Complete step by step solution:
A simultaneous throw of two dice is given and are asked to find the probability when then sum of the observations on the two dice are 11.
We know that the formula for probability of any event is equal to:
$\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$
The total outcomes are calculated by multiplying 6 by 6 because in one throw of a dice, 6 outcomes can be possible (1, 2, 3, 4, 5 and 6). So, in the simultaneous throw of two dice, 6 multiplied by 6 possibilities are there.
$6\times 6=36$
Hence, the total outcomes are 36.
The favorable outcomes are those outcomes in which the sum of the numbers appear on the two dice is 11.
So, the possible cases in which sum of the numbers appear on the face of the two dice are 11 as follows:
(5, 6) and (6, 5)
Hence, there are two favorable outcomes.
Now, substituting the values of total outcomes and favorable outcomes in the formula of probability we get,
$\text{Probability}=\dfrac{2}{36}$
Now, you can see that the numerator and denominator is divisible by 2 so dividing the numerator and the denominator by 2 we get,
$\text{Probability}=\dfrac{1}{18}$

Hence, when the two dice simultaneously thrown then the probability of getting the sum as 11 is $\dfrac{1}{18}$.

Note: The mistake that could be possible in the above problem is that you might forget to consider the two possibilities in which the sum of the numbers appeared on the dice is 11 and the case which you forget is written as follows:
(5, 6) and (6, 5)
These are the two possible cases, you might forget either of these two cases so make sure you won’t make this mistake.