An ordinary die is thrown. Find the probability that the number obtained is even or greater than 4?

Решение

A n or d ina ry d i e i s t h ro w n . F in d t h e p ro babi l i t y t ha t t h e n u mb er o b t ain e d i s e v e n or g re a t er t han 4 ?

\frac{2}{3}

десятичными цифрами

0.66666 \dots

Шаги решения

Find the probability of the number obtained is even:

\frac{1}{2}

Find the probability of greater than 4:

\frac{1}{3}

Find the probability of the number obtained is even and greater than 4:

\frac{1}{6}

Use the Inclusion-Exclusion formula

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

= \frac{1}{2} + \frac{1}{3} - \frac{1}{6}

\frac{1}{2} + \frac{1}{3} - \frac{1}{6} = \frac{2}{3}

= \frac{2}{3}