Dice Rolling Six Probability

Three players roll the dice. They can start the game when a six is rolled. Everyone rolls 1 time.
a) What is the probability that exactly one starts in the first round?
b) What is the probability that at least two start?

Final Answer:

p₁ =  0.3472
p₂ =  0.0741

Step-by-step explanation:

$$\begin{gathered} q=1/6=\frac{1}{6}\doteq 0.1667 \\ {p}_1=3\cdot q\cdot (1-q)\cdot (1-q)=3\cdot 0.1667\cdot (1-0.1667)\cdot (1-0.1667)=0.3472 \end{gathered}$$

$p_2=q\cdot q\cdot q+3\cdot q\cdot q\cdot (1-q)=0.1667\cdot 0.1667\cdot 0.1667+3\cdot 0.1667\cdot 0.1667\cdot (1-0.1667)=0.0741$

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