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(i)

(a)

P(faulty)

= P(made by A and faulty) + P(made by B and faulty)

= 0.6(0.05) + 0.4(0.07)

= 0.058

(b)

P(made by A | faulty)

=

=

=

(ii)

(a)

P(exactly one of them is faulty)

=

= 0.109272 (exact)

(b)

P(both were made by A | exactly one is faulty)

=

=

=

=

### KS Comments:

Question can be easily solved by drawing a tree diagram. Do take note that we only wrong off NON exact answers to 3sf, so for (iia), we keep the full exact answer.