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Read the following caselet and choose the best alternative
A teacher wanted to administer a multiple choice (each question having six choices) based quiz of high difficulty level to a class of sixty students. The quiz had sixty questions. The probability of selecting the correct answer for a good student and a brilliant student was 0.2 and 0.25 respectively. The poor students had no learning advantage. The teacher did not want students to cheat but does not have time and resources to monitor. All students were seated serially in 10 rows and 6 columns.
Three good students were seated next to each other. What is the probability of them having the same incorrect choice for four consecutive questions?
Probability of the first student of the group of three getting 4 incorrect answer of 1st question = $$\frac{4}{5}$$
Probability of the second student of the group getting the same incorrect answer of 1st question as that of the first student = $$\frac{4}{5}\times\ \frac{1}{5}$$
Probability of the third student of the group getting the same incorrect answer of 1 st question as that of the first student = $$\frac{4}{5}\times\ \frac{1}{5}$$
Therefore, the probability of all the three getting same incorrect answer of 1st question = $$\frac{4}{5}\times\frac{4}{5}\times\frac{1}{5}\times\frac{4}{5}\times\frac{1}{5}=\frac{4^3}{5^5}$$
Hence, the probability = $$\left(\frac{4^3}{5^5}\right)^4$$
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