MATHEMATICS · Multi-part · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions
Problem
A safety device is fitted with five identical, independent sensors. Each sensor works during a test with probability 0.85. The device issues an alarm if at least three sensors work.
(i) Find the probability that the device issues an alarm.
(ii) Determine the probability that exactly three sensors work.
(iii) If the device has issued an alarm, calculate the probability that exactly three sensors worked.