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Probability

Question

Wired Faculty App

Find the probability distribution of the sum of numbers obtained when two dice are thrown.

Solution

Let X denote the sum of the numbers obtained on the two dice. X can take values 2, 3, ......, 12

straight P left parenthesis straight X space equals space 2 right parenthesis space equals space straight P open curly brackets left parenthesis 1 comma space 1 right parenthesis close curly brackets space equals space 1 over 36 straight P left parenthesis straight X space equals space 3 right parenthesis space equals space straight P open curly brackets left parenthesis 1 comma space 2 right parenthesis comma space left parenthesis 2 comma space 1 right parenthesis close curly brackets space equals 2 over 36 straight P left parenthesis straight X space equals space 4 right parenthesis space equals space straight P left curly bracket left parenthesis 1 comma space 3 right parenthesis comma space left parenthesis 2 comma space 2 right parenthesis comma space left parenthesis 3 comma space 1 right parenthesis right curly bracket space equals space 3 over 36 straight P left parenthesis straight X space equals space 5 right parenthesis space equals space straight P left curly bracket left parenthesis 1 comma space 4 right parenthesis comma space left parenthesis 2 comma space 3 right parenthesis comma space left parenthesis 3 comma space 2 right parenthesis comma space left parenthesis 4 comma space 1 right parenthesis right curly bracket space equals space 4 over 36 straight P left parenthesis straight X space equals space 6 right parenthesis space equals space straight P left curly bracket left parenthesis 1 comma space 5 right parenthesis comma space left parenthesis 2 comma space 4 right parenthesis comma space left parenthesis 3 comma space 3 right parenthesis comma space left parenthesis 4 comma space 2 right parenthesis comma space left parenthesis 5 comma space 1 right parenthesis right curly bracket space equals space 5 over 36 straight P left parenthesis straight X space equals space 7 right parenthesis space equals space straight P left curly bracket left parenthesis 1 comma space 6 right parenthesis comma space left parenthesis 2 comma space 5 right parenthesis comma space left parenthesis 3 comma space 4 right parenthesis comma space left parenthesis 4 comma space 3 right parenthesis comma space left parenthesis 5 comma space 2 right parenthesis comma space left parenthesis 6 comma space 1 right parenthesis space equals space 6 over 36 straight P left parenthesis straight X space equals space 8 right parenthesis space equals space straight P left curly bracket left parenthesis 2 comma space 6 right parenthesis comma space left parenthesis 3 comma space 5 right parenthesis comma space left parenthesis 4 comma space 4 right parenthesis comma space left parenthesis 5 comma space 3 right parenthesis comma space left parenthesis 6 comma space 2 right parenthesis space equals space 5 over 36 straight P left parenthesis straight X space equals space 9 right parenthesis space equals space straight P left curly bracket left parenthesis 3 comma space 6 right parenthesis comma space left parenthesis 4 comma space 5 right parenthesis comma space left parenthesis 5 comma space 4 right parenthesis comma space left parenthesis 6 comma space 3 right parenthesis right curly bracket space equals space 4 over 36 straight P left parenthesis straight X space equals space 10 right parenthesis space equals space straight P left curly bracket left parenthesis 4 comma space 6 right parenthesis comma space left parenthesis 5 comma space 5 right parenthesis comma space left parenthesis 6 comma space 4 right parenthesis right curly bracket space equals space 3 over 36 straight P left parenthesis straight X space equals space 11 right parenthesis space equals space straight P left curly bracket left parenthesis 5 comma space 6 right parenthesis comma space left parenthesis 6 comma space 5 right parenthesis right curly bracket space equals space 2 over 36 straight P left parenthesis straight X space equals space 12 right parenthesis space equals space straight P left curly bracket left parenthesis 6 comma space 6 right parenthesis right curly bracket space equals space 1 over 36

Probability distribution of X is

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