A die is rolled twice. Find the probability of getting both odd numbers or the same number on both rolls

Решение

A d i e i s ro ll e d tw i ce . F in d t h e p ro babi l i t y o f g e tt in g b o t h o dd n u mb ers or t h e s am e n u mb er o n b o t h ro ll s

\frac{1}{3}

десятичными цифрами

0.33333 \dots

Шаги решения

Find the probability of getting both odd numbers:

\frac{1}{4}

Find the probability of the same number on both rolls:

\frac{1}{6}

Find the probability of getting both odd numbers and the same number on both rolls:

\frac{1}{12}

Use the Inclusion-Exclusion formula

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

= \frac{1}{4} + \frac{1}{6} - \frac{1}{12}

\frac{1}{4} + \frac{1}{6} - \frac{1}{12} = \frac{1}{3}

= \frac{1}{3}