Probability 80857

During the exam, the student answers 4 questions out of 25. He is ready for 20 of them. Find the probability that he draws exactly one that he does not know.

Correct answer:

p =  0.4096

Step-by-step explanation:

$$\begin{gathered} p_0=20/25=\frac{4}{5}=0.8 \\ p=\left(\genfrac{}{}{0ex}{}{4}{3}\right)\cdot p_0^3\cdot (1-p_0{)}^{4-3}=(\genfrac{}{}{0ex}{}{4}{3})\cdot 0.8^3\cdot (1-0.8{)}^{4-3}=4\cdot 0.8^3\cdot 0.2^1=0.4096 \end{gathered}$$

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