Answer to Question #145613 in Statistics and Probability for SHIVA N

Question

At the end of a production process, 500 electrical components pass through three quality
checks: P, Q and R. It is found that 38 components fail check P, 29 fail Q, 30 fail R, 7 fail P
and Q, 5 fail Q and R, 8 fail R and P, and 3 fail all checks. Determine how many components:
(a) pass all checks,
(b) fail exactly one check,
(c) fail exactly two checks.

Answer 1

We draw a following venn diagram from the data given:

a) Number of pass all check= 500- (26+20+20+4+5+2+3)=420

b)Number of fail exactly one check= 26+20+20=66

c) Number of fail exactly two checks= 4+5+2=11