Question

Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as:
six appears on at least one die

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Solution

Let X be the random variable, which takes values 0, 1.

straight P left parenthesis straight X space equals space 0 right parenthesis space equals space straight P left parenthesis no space six right parenthesis space space space space space space space space space space space space space space space space space space equals space left curly bracket 1 space minus space straight P left parenthesis getting space straight a space six space on space straight a space single space throw right parenthesis right curly bracket space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space cross times space left curly bracket 1 minus straight P left parenthesis getting space straight a space six space on space single space throw right parenthesis right curly bracket space space space space space space space space space space space space space space space space equals space open parentheses 1 minus 1 over 6 close parentheses space open parentheses 1 minus 1 over 6 close parentheses space equals 25 over 36

and

straight P left parenthesis straight X space equals space 1 right parenthesis space equals space straight P left parenthesis six space on space at space least space one space throw right parenthesis space space space space space space space space space space space space space space space space equals space 1 space minus space straight P left parenthesis not space getting space straight a space six space on space any space throw right parenthesis space space space space space space space space space space space space space space space space equals space 1 minus 5 over 6 cross times 5 over 6 space equals 11 over 36

∴ probability distribution of X is

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