A radar system can detect an enemy plane in one out of 10 consecutive scans. The probability that it cannot detect an enemy plane at least two times in four consecutive scans, is

Step-by-step solution

gathered X_i= cases 1 ; & if target is detected 0 ; & if target is not detected cases p(x)= cases 0.1 & ; 0.9=1 & x=0 cases gathered Now, each X _ i is independent trial with p=0.1P (target will be detected at least two times in 4 consecutive scans )= ^4 C ₂(0.1)^2(0.9)^2+ ^4 C ₃(0.1)^3(0.9)^1+ ^4 C ₄(0.1)^4(0.9)^0=0.0523 So, required probability =1-0.0523=0.9477