5. A manufactured component has its quality graded on its performance, appearance and cost.
Each of these 3 characteristics is graded as either pass or fail. There is a probability of
0.4 that a component passes on both appearance and cost. There is a probability of 0.31
that a component passes on all 3 characteristics. There is a probability of 0.64 that a
component passes on performance. There is a probability of 0.19 that a component fails on
all 3 characteristics. There is a probability of 0.06 that a component passes on appearance
but fails on both performance and cost.
(a) What is the probability that a component passes on cost but fails on both performance
and appearance?
(b)
If a component passes on both appearance and cost, what is the probability that it
passes on all 3 characteristics?