MATHEMATICS · Subjective · CBSE · Mathematics · Probability · Probability
Problem
Three independent security cameras monitor a gate. When an intruder passes, camera C1 detects the intruder with probability 0.8, camera C2 with probability 0.7, and camera C3 with probability 0.6. Each camera operates whether or not the others detect the intruder. An alarm is raised if at least one camera detects the intruder.
(i) Calculate the probability that none of the three cameras detects the intruder.
(ii) Hence find the probability that the alarm is raised.
(iii) If the alarm is raised, determine the probability that exactly two cameras detected the intruder.