A car must clear three quality checkpoints before it leaves an assembly plant
MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
A car must clear three quality checkpoints before it leaves an assembly plant. The probability that it passes the first checkpoint is 0.90. If it passes the first checkpoint, the probability that it passes the second checkpoint is 0.95. If it passes the first two checkpoints, the probability that it passes the third checkpoint is 0.96.
(i) Calculate the probability that a randomly chosen car passes all three checkpoints.
(ii) Determine the probability that the car passes the first two checkpoints but fails at the third checkpoint.
(iii) Find the probability that the car fails at least one of the three checkpoints.