Card number probability

On ten identical cards, there are numbers from zero to nine. Determine the probability that a two-digit number randomly drawn from the given cards is:
a) even
b) divisible by six
c) divisible by twenty-one

Final Answer:

p₁ =  0.5062
p₂ =  0.1728
p₃ =  0.0494

Step-by-step explanation:

$$\begin{gathered} n=9\cdot 1+8\cdot 9=81 \\ {n}_1=9\cdot 1+(5+3)\cdot 4=41 \\ {p}_1=\frac{n_1}{n}=\frac{41}{81}=0.5062 \end{gathered}$$

$$\begin{gathered} n_2=3\cdot 1+3\cdot 4-1=14 \\ {p}_2=\frac{n_2}{n}=\frac{14}{81}=0.1728 \end{gathered}$$

$$\begin{gathered} 21;42;63;84 \\ {n}_3=4 \\ {p}_3=\frac{n_3}{n}=\frac{4}{81}=0.0494 \end{gathered}$$

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