## Mutually Independent Dice Rolls

Consider the following events the rolling 3 dice:

Which of the following events are mutually independent?

Home » Courses » Electrical Engineering and Computer Science » Mathematics for Computer Science » Unit 4: Probability » 4.3 Independence & Causality » 4.3.4 Mutually Independent Dice Rolls

Consider the following events the rolling 3 dice:

Which of the following events are mutually independent?

Three dice throws are mutually independent. Any pair of dice throws is also independent.
\(\Pr[A_1 \cap S_3]= \Pr[A_1 \cap B_1 \cap C_1]=\frac{1}{216}\neq \frac{1}{6}\cdot\frac{1}{216}=\Pr[A_1]\Pr[S_3].\)
\(\Pr[A_1 \cap B_1 \cap S_7]= \Pr[A_1 \cap B_1 \cap C_5]=\frac{1}{216}\neq \frac{1}{6}\cdot\frac{1}{6}\cdot\frac{15}{216}=
\Pr[A_1]\Pr[B_1]\Pr[S_7].\)
\(\Pr[A_1 \cap B_1 \cap S_8]= \Pr[A_1 \cap B_1 \cap C_6]=\frac{1}{216}\neq \frac{1}{6}\cdot
\frac{1}{6}\cdot\frac{21}{216}=\Pr[A_1]\Pr[B_1]\Pr[S_8].\)