Sheldon Ross Introductory Statistics - Probability Section 4.3

1.
(a) P(E) = 0.35 P(F) = 0.65 P(G) = 0.55
(b) P (E∪F) = 1
(c) P(E ∪ G) = 0.80
(d) P(F ∪ G) = 0.75
(e) P(E ∪ F ∪ G) = 1
(f) P(E ∩ F) = 0
(g) P(F ∩ G) = 0.45
(h) P(E ∩ G) = 0.1
(i) P(E ∩ F ∩ G) = 0.45

2.
(a) P(A) ^c = 0.8
(b) P(A ∪ B) = 0.7
(c) P(A ∩ B) = 0 (disjoint events)
(d) P(Ac ∩ B) = 0.5

3. 0.0001

4.
(a) P1+P2+P3 = 0.86
(b) 0.16

5.
(a) No
(b) Yes (they have overlap)

6. 1/3

7.
(a) 1100 trees - 1.0 (demand is never less than 1100!)
(b) 1400 trees - 0.8
(c) 1600 trees - 0.5
(d) 2000 trees - 0.1

8.
(a) 2 or fewer defects - 0.55
(b) 4 or more defects - 0.25
(c) Between (inclusive) 1 and 3 defects - 0.63
(d) 0.9
(e) 0.55

9.
(a) 3 or fewer errors - 0.95
(b) 2 or fewer errors - 0.80
(c) 0 errors - 0.20

10.
(a) 0.099
(b) 0.131
(c) P(80s + 90s + 100s) = 0.467

11. 0.7 (using addition rule)

12. 34%

13. 30 + 3 - 2 = 31 %

14.
(a) 0.082
(b) 0.918

15. 0.6

16.
(a) 14
(b) Both Stats and Phys - 14

17.
(a) I - A ∩ B^c
(b) II - A ∩ B
(c) III - B ∩ A ^c
(d) P(A ∪ B) = P(1) + P (3) - P(2)
(e) P(A) - P(1) + P(2)
(f) P(B) - P(2) + P(3)
(g) P(A ∩ B) = P(2)