For an initial screening of an admission test, a candidate is given fifty problems to solv…

Question

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability
that the candidate solve any problem is $${4 \over 5}$$
, then the probability that he is unable to solve less than two
problems is :

Accepted Answer

There are 50 questions in an exam.

So Probability of each question to be correct is p = $${4 \over 5}$$

and also probability of each question to be incorrect is q = $${1 \over 5}$$

Let Y is the number of correct question in 50 questions, hence required probability is

$${\left( {{4 \over 5}} \right)^{50}} + {}^{50}{C_1}\left( {{1 \over 5}} \right){\left( {{4 \over 5}} \right)^{49}}$$

= $${\left( {{4 \over 5}} \right)^{49}} + \left( {{4 \over 5} + 10} \right)\left( {{4 \over 5}} \right)$$

= $${{54} \over 5}{\left( {{4 \over 5}} \right)^{49}}$$

Solutions · 1