Question

In a school machine shop, 60% of all machine breakdowns occur on lathes and 15% occur on drill presses. Let E denote the event that the next machine breakdown is on a lathe, and let F denote the event that a drill press is the next machine to break down. With P(E) = .60 and P(F) = .15, calculate: P(Eᶜ ∩ Fᶜ) 6.91 There are five faculty members in a certain academic department. These individuals have 3, 6, 7, 10, and 14 years of teaching experience. Two of these individuals are randomly selected to serve on a personnel review committee. What is the probability that the chosen representatives have a total of at least 15 years of teaching experience? (Hint: Consider all possible committees.) 6.92 The general addition rule for three events states that P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C) A new magazine publishes columns entitled “Art” (A), “Books” (B), and “Cinema” (C). Suppose that 14% of all subscribers read A, 23% read B, 37% read C, 8% read A and B, 9% read A and C, 13% read B and C, and 5% read all three columns. What is the probability that a randomly selected subscriber reads at least one of these three columns? 6.93 A theater complex is currently showing four R-rated movies, three PG-13 movies, two PG movies, and one G movie. The following table gives the number of people at the first showing of each movie on a certain Saturday: Number of Theater Rating Viewers 1 R 600 2 PG-13 420 3 PG-13 323 4 R 196 5 G 254 6 PG 179 7 PG-13 114 8 R 205 9 R 139 10 PG 87

          In a school machine shop, 60% of all machine breakdowns
occur on lathes and 15% occur on drill presses. Let
E denote the event that the next machine breakdown is on a
lathe, and let F denote the event that a drill press is the next
machine to break down. With P(E) = .60 and P(F) = .15,
calculate:
P(Eᶜ ∩ Fᶜ)

6.91 There are five faculty members in a certain academic
department. These individuals have 3, 6, 7, 10, and 14
years of teaching experience. Two of these individuals are
randomly selected to serve on a personnel review committee.
What is the probability that the chosen representatives
have a total of at least 15 years of teaching experience?
(Hint: Consider all possible committees.)

6.92 The general addition rule for three events states that
P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C)
A new magazine publishes columns entitled “Art” (A),
“Books” (B), and “Cinema” (C). Suppose that 14% of all
subscribers read A, 23% read B, 37% read C, 8% read A
and B, 9% read A and C, 13% read B and C, and 5% read
all three columns. What is the probability that a randomly
selected subscriber reads at least one of these three
columns?

6.93 A theater complex is currently showing four R-rated
movies, three PG-13 movies, two PG movies, and one G
movie. The following table gives the number of people at
the first showing of each movie on a certain Saturday:
Number of
Theater Rating Viewers
1 R 600
2 PG-13 420
3 PG-13 323
4 R 196
5 G 254
6 PG 179
7 PG-13 114
8 R 205
9 R 139
10 PG 87

Added by Vinodhini J.

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