# A die is rolled 10 times. What is the probability of the sum of the faces being equal to 27? (Hint: use generating functions)

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A die is rolled 10 times. What is the probability of the sum of the faces being equal to 27? (Hint: use generating functions)

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Step 1

Here a die is rolled 10 times and this is similar of 10 dice at a time as one  roll of a die is independent of another roll.

So here let us assume 10 dice are rolled once and we need probability of sum equal to 27.

When a die is rolled it can have any number among 1,2,3,4,5,6. Let Xi represent the outcome when a die is rolled. Its probability distribution and moment generating function are given below

Step 2

Here all random variables X1 X2 X 3....X10 are independent random variables. So the moment g...

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