Probability — test

A test contains questions with four answer options, exactly one of which is correct. To pass the exam successfully, at least half of the questions must be answered correctly. How many questions should the test contain so that the probability of a student who chooses answers randomly (where each answer has equal probability) passing the exam is less than 0.01?

Final Answer:

n =  8

Step-by-step explanation:

$$\begin{gathered} p=0.01 \\ {p}_1=1/4=\frac{1}{4}=0.25 \\ {p}_1^n<p \\ n\cdot \log p_1>\log p \\ {n}_1=\log p/\log (p_1)=\log 0.01/\log 0.25\doteq 3.3219 \\ n=2\cdot \lceil n_1\rceil =2\cdot \lceil 3.3219\rceil =8 \end{gathered}$$

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