3) Quality control of an automobile transmission, at a particular manufacturing

Question

3) Quality control of an automobile transmission, at a particular manufacturing plant, requires
that it passes at least two out of three extreme pressure tests. Let P denote the event that an
test is passed, and P c be the event that the test is not passed. A given transmission’s results can
then be characterized by a sequence such as PPP c, which means that the third test was not
passed, while the first and second tests were passed (this transmission would pass the quality
control requirements).
a) List the elements of the sample space of all possible outcomes for a transmission.
b) List the elements that constitute each of the following events;
A: the transmission passes at least one test,
B: the transmission passes at least two tests,
C: the transmission passes only one test.
ENGM2032, Applied Probability and Statistics Assignment #1 Fall 2017: pg 2
c) Are A and B disjoint? Why or why not?
d) Are B and C disjoint? Why or why not?
e) List the elements that constitute each of the following events and describe these events in
words (for example, for Ac, you might say “the transmission fails all three tests”):
i) Bc
ii) Cc
iii) A [ C
iv) A C
v) A B Cc
vi) (B [ C)c
vii) A Ac

Explanation / Answer

c) No, A and B is the transmission passes at least one test and at least two test
Therefore, the transmission passes at least one test
d) Yes, B and C is the transmission passes at least two tests and only one test
Therefore, B and C is null
e)i) Bc means that the transmission fails at least two tests
ii) Cc means that the transmission fails only one test
iii) A and C is the transmission passes at least one test and only one test
Therefore, A and C is null
iv) A/C is that the transmission passes at least one test happend whne the transmission passes only one test is already happend

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