MATHEMATICS · Subjective · CBSE · Mathematics · Probability · Probability
Problem
During a fire drill, two identical smoke detectors D1 and D2 are placed in the same corridor. Each detector works independently and has probability 0.92 of sounding when smoke is present. The corridor alarm rings if at least one detector sounds.
(i) Describe, in words, the two complementary events involved when deciding whether the corridor alarm rings.
(ii) Give a clear reason, without using numerical calculations, why the probability that the alarm rings equals 1 minus the probability that both detectors fail to sound.
(iii) Calculate the numerical probability that the corridor alarm rings when smoke is present.