MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
In a garden lighting arrangement, two identical bulbs are wired in parallel so that at least one must glow for illumination. Each bulb functions independently with probability 0.9 on a given night. The parallel bulb unit is controlled by an electronic switch that must also work for light to be supplied. The switch operates independently with probability 0.98.
(i) Find the probability that the garden is illuminated on a given night.
(ii) If the switch is replaced by a higher-quality one that works with probability 0.995, calculate the new probability that the garden is illuminated.
(iii) Express, to two decimal places, the percentage increase in reliability obtained by installing the new switch.