Question

For an initial screening of an entrance exam, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is \( \frac{4}{5} \), then the probability that he is unable to solve less than two problems is

• A. $\frac{201}{5}\left(\frac{1}{5}\right)^{49}$
• B. $\frac{316}{25}\left(\frac{4}{5}\right)^{48}$
• C. $\frac{54}{5}\left(\frac{4}{5}\right)^{49}$
• D. $\frac{164}{25}\left(\frac{1}{5}\right)^{48}$

Hint:

Probability Tip:Pay close attention to phrasing: "unable to solve" flips the definitions of $p$ and $q$ from how they are initially presented in the text. "Less than two" strictly means 0 and 1. It does not include 2.

Answer 1

The Correct Option is C