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What is the probability that the total of two dice will be greater than 9, given that the first die is a 5?

Answer Verified Verified
Hint: We will use the definition of the probability to solve this question. We will list all the possible outcomes and then we will use the formula of 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 the total dice thrown are 2. And when the first die is rolled, we get a 5.
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.
First, we will list the total outcomes when there is a 5 on the first die.
So, the total outcomes will be: {(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)}
Now, we are given a condition that we need to find the probability that the total of two dice will be greater than 9.
So, the possible outcomes which has a total greater than 9 are: {(5, 5), (5, 6)}
Using the definition of probability,
Probability = the total number of possible outcomes /the total number of outcomes
Substituting the value, we get
Probability = $\dfrac{2}{6} = \dfrac{1}{3}$
Hence, the probability of getting the total of two dice greater than 9 is $\dfrac{1}{3}$.

Note: You can also solve this question by using the method of conditional probability. 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 0.333 which is between 0 and 1.