Maroš

Maroš draws two cards from a deck of Mariáš cards (32 cards). What is the probability that he draws a seven or an ace, but not the green seven?

Final Answer:

p =  0.38

Step-by-step explanation:

$$\begin{gathered} C_2(31)=\left(\genfrac{}{}{0ex}{}{31}{2}\right)=\frac{31!}{2!(31-2)!}=\frac{31\cdot 30}{2\cdot 1}=465 \\ {C}_2(24)=\left(\genfrac{}{}{0ex}{}{24}{2}\right)=\frac{24!}{2!(24-2)!}=\frac{24\cdot 23}{2\cdot 1}=276 \\ 32cards=4\times 8-4\times (7,8,9,10,J,Q,K,A) \\ n=4\cdot 8=32 \\ {n}_0=\left(\genfrac{}{}{0ex}{}{n}{2}\right)=496 \\ {C}_2(32)=\left(\genfrac{}{}{0ex}{}{32}{2}\right)=\frac{32!}{2!(32-2)!}=\frac{32\cdot 31}{2\cdot 1}=496 \\ {n}_1=\left(\genfrac{}{}{0ex}{}{n-1}{2}\right)=\left(\genfrac{}{}{0ex}{}{32-1}{2}\right)=465 \\ {n}_2=\left(\genfrac{}{}{0ex}{}{n-2\cdot 4}{2}\right)=\left(\genfrac{}{}{0ex}{}{32-2\cdot 4}{2}\right)=276 \\ {n}_3=n_1-n_2=465-276=189 \\ p=\frac{n_3}{n_0}=\frac{189}{496}=0.38 \end{gathered}$$

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