For an entry to a certain course, a candidate is given twenty problems to solve. If the probability that the candidate can solve any problem is 3 7 , then the probability that he is unable to solve at most two problem is

Step-by-step solution

( q = ) probability that the candidate can solve the problem (= 3 7 ) ( p =1- 3 7 = 4 7 ) Also, ( n =20 ). ( aligned & Required probability & = P ( X 2) & = P ( X =0)+ P ( X =1)+ P ( X =2) & = ²⁰ C ₀ p ²⁰ q ^0+ ²⁰ C ₁ p ¹⁹ q + ²⁰ C ₂ p ¹⁸ q ^2 & =1 ( 4 7 )²⁰ ( 3 7 )^0+20 ( 4 7 )¹⁹ ( 3 7 )+190 ( 4 7 )¹⁸ ( 3 7 )^2 & = ( 4 7 )¹⁸ [ 16 49 + 240 49 + 1710 49 ] & = ( 4 7 )¹⁸ 1966 49 aligned )