Use the addition rule to find the probability of the following event: Obtaining a sum of 6 or doubles (same number on each die) when a pair of dice is rolled once. Express your answer as a decimal rounded to 1 decimal place.

Solution

Solution

\frac{5}{18}

Solution steps

Find the probability of the following event : Obtaining a sum of 6:

\frac{5}{36}

Find the probability of the sum doubles ( same number on each die ) when a pair of dice is rolled once:

\frac{1}{6}

Find the probability of the following event : Obtaining a sum of 6 and the sum doubles ( same number on each die ) when a pair of dice is rolled once:

\frac{1}{36}

Use the Inclusion-Exclusion formula

P (X \lor Y) = P (X) + P (Y) - P (X \land Y)

= \frac{5}{36} + \frac{1}{6} - \frac{1}{36}

\frac{5}{36} + \frac{1}{6} - \frac{1}{36} = \frac{5}{18}

= \frac{5}{18}

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