In 2012, the Anchuria School Board decided that three questions were too few. Now, one needs to correctly answer six questions out of 40. The question is, if one knows nothing and simply guesses the answers, in which year is the probability of obtaining the Anchurian certificate higher - in 2011 or in 2012?
If a graduate guesses the answers, the Unified State Exam (EGE) can be considered as a Bernoulli scheme with a success probability $p=$ 0.25 and a failure probability $q=0.75$. In 2011, to pass the exam, one needed to answer at least three questions correctly. It is more convenient to find the probability of the opposite event, that is, the probability of answering fewer than three questions correctly. This is equal to the sum of the probabilities that the graduate answered 0, 1, and 2 questions correctly, that is, $\quad \sum_{k=0}^{2} C_{20}^{k} p^{k} q^{20-k} \approx 0.091 ;$ therefore, the probability of passing the exam is approximately 0.909.

Similarly, we find that in 2012, the probability of failing the exam is the probability of passing the exam is approximately $0.957$.

## Answer

In 2012.

Submit a comment