When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that either doubles are rolled or the sum of the dice is 8

解

Wh e n tw o ba l an ce d d i ce a re ro ll e d, t h ere a re 36 p oss ib l e o u t co m es . F in d t h e p ro babi l i t y t ha t e i t h er d o u b l es a re ro ll e d or t h e s u m o f t h e d i ce i s 8

\frac{5}{18}

十進法表記

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解答ステップ

Find the probability of either doubles are rolled:

\frac{1}{6}

Find the probability of the sum of the dice is 8:

\frac{5}{36}

Find the probability of either doubles are rolled and the sum of the dice is 8:

\frac{1}{36}

Use the Inclusion-Exclusion formula

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

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

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

= \frac{5}{18}