Two dice are thrown simultaneously. Find the probability of getting the sum of the two numbers on the dice is greater than 6 but less than 9.

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Detailed Solution

Given that two dice are thrown simultaneously.
We have to find the probability that the sum of the numbers obtained is greater than 6 but less than 9.
Probability of an event E is defined as:

P (E) = \frac{Number of favorable outcomes}{Total number of possible outcomes}

The possible outcomes, when a pair of dice is tossed together, are:
Question Image

Total number of possible outcomes will be 36.
According to the question, favorable outcomes are the numbers obtained who have the sum greater than 6 but less than 9.
Thus we have:

1, 6, 6, 1, 2, 5, 5, 2, 3, 4, 4, 3, 4, 4, 2, 6, 6, 2, 3, 5, 5, 3

Hence, the number of favorable outcomes =11.
Let

E

be the event that the sum of the numbers obtained is greater than 6 but less than 9.
Now, the probability that sum of the numbers obtained is greater than 6 but less than 9 is: