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 4 5 , then the probability, that he is unable to solve less than two problems, is

Step-by-step solution

q= Probability that the candidate can solve any problem = 4 5 p =1- 4 5 = 1 5 Also, n =50 aligned & Required probability = P ( X < 2) & = P ( X =0)+ P ( X =1) & = ⁵⁰ C ₀ ( 1 5 )^0 ( 4 5 )⁵⁰+ ⁵⁰ C ₁ ( 1 5 )^1 ( 4 5 )⁴⁹ & = ( 4 5 )⁵⁰+50 ( 1 5 ) ( 4 5 )⁴⁹ & = ( 4 5 + 50 5 ) ( 4 5 )⁴⁹ & = ( 54 5 ) ( 4 5 )⁴⁹ aligned