In a factory quality check

MATHEMATICS · Subjective · A Level · Mathematics · Probability · Probability

Problem

In a factory quality check, three successive tests are conducted on each product. Event

A

: product passes the visual inspection, with

P(A)=0.90

. Event

B

: product meets weight specifications, with

P(B)=0.80

. Events

A

and

B

are independent. Event

C

: product passes the performance test, and

P(C\mid A\cap B)=0.50

. Calculate the probability that a randomly chosen product passes all three tests

A

B

and

C