The probability that an event does not happen in one trial is 0.8 The probability that the event happens atmost once in three trials is

Step-by-step solution

Given, p=0.2, q=0.8, n=3 From binomial distribution, P(X=r)= ^n C₂ P^r q^ n-r Probability that event happens at most once, P(X 1)=P(X=0)+P(X=1) aligned & = ^3 C₀(0.2)^0(0.8)³⁻⁰+ ^3 C₁(0.2)^1(0.8)³⁻¹ & = 3 ! 0 ! 3 ! 1 ( 8 10 )^3+ 3 ! 1 ! 2 ! ( 2 10 ) ( 8 10 )^2 & = 64 125 + 48 125 = 112 115 =0.896 aligned