In a trial, the probability of success is twice the probability of failure. In six trials, the probability of at most two failure will be

Step-by-step solution

Let the probability of failure and success be p and q , respectively. Let X represents the number of failure According to the question, q=2 p p+q=1 and q=2 p p= 1 3 and q= 2 3 Now, required probability =P(X 2) aligned & =P(X=0)+P(X=1)+P(X=2) & = ^6 C₀ p^0 q^6+ ^6 C₁ p^1 q^5+ ^6 C₂ p^2 q^4 & = ( 2 3 )^6+6 ( 1 3 )^1 ( 2 3 )^5+15 ( 1 3 )^2 ( 2 3 )^4 & = 1 729 (64+192+240)= 496 729 aligned