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MATH 352 HW3_solutions

# MATH 352 HW3_solutions - (i No events A and B are not...

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Homework Solutions Homework #3 Section 2.1 2. (a) S={1, 2, 3, 4} or S={1,1,2,2,2,3,3,4} (second is more convenient for probability computations) (b) P (even number)= P (2) + P (4) = 3/8 + 1/8 = 1/2 (c) No, the set of possible outcomes is still {1, 2, 3, 4}. (d) Yes, P(even number) = P(2) + P(4) = 3/9 + 2/9 = 5/9 4. (a) { (R, G, R) (R, G, Y) (R, G, G) (R, R, R,) (R, R, Y) (R, R, G) (R, Y, R) (R, Y, Y) (R, Y, G) (Y, G, R) (Y, G, Y) (Y, G, G) (Y, R, R) (Y, R, Y) (Y, R, G) (Y, Y, R) (Y, Y, Y) (Y, Y, G) (G, G, R) (G, G, Y) (G, G, G) (G, R, R) (G, R, Y) (G, R, G) (G, Y, R) (G, Y, Y) (G, Y, G) } (b) A = {(R, R, R) (Y, Y, Y) (G, G, G)} (c) B = {(R, G, Y) (R, Y, G) (Y, G, R) (Y, R, G) (G, R, Y) (G, Y, R)} (d) C = {(R, G, G) (Y, G, G) (G, G, R) (G, G, Y) (G, G, G) (G, R, G) (G, Y, G)} (e) A n C = {(G, G, G)} (f) A U B = {(R, R, R) (Y, Y, Y) (G, G, G) (R, G, Y) (R, Y, G) (Y, G, R) (Y, R, G) (G, R, Y) (G, Y, R)} (g) A n C c = {(R, R, R) (Y, Y, Y)} (h) A c n C = {(R, G, G) (Y, G, G) (G, G, R) (G, G, Y) (G, R, G) (G, Y, G)}

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Unformatted text preview: (i) No, events A and B are not mutually exclusive because both events contain the outcome (G, G, G). (j) Yes, events B and C are mutually exclusive because the two events have no outcomes in common. 6. (a) We list here the pairs of bolts using their numbers, these are equaly likely outcomes S={(1, 2) (1, 3) (1, 4) (2,1) (2, 3) (2, 4) (3, 1) (3, 2) (3, 4) (4, 1) (4, 2) (4, 3)} Hence, the probability of each outcome is 1/12. (b) P (both are 7mm) = P{(3, 4) or (4, 3)}= 2/12= 1/6 (c) P (one is 5mm and one is 7mm) = P{(1, 3) (1, 4) (2, 3) (2, 4) (3, 1) (3, 2) (4, 1) (4, 2 )} = 8/12= 2/3. 8. (a) False (b) True (c) True. All answers are explained by the frequency interpretation of probability. 10. (a) P ( E U T ) = P (E) + P (T) – P (E n T)= 0.11 (b) P ( E c U T c ) = 1 - P ( E U T ) = 1 - 0.11 = 0.89 (c) Need to find P ( E n T c ). We know by looking at a Venn diagram that P (E)= P (E n T) + P ( E n T c ). We are given that P (E) = 0.10 and P (E n T) = 0.01. Therefore, P ( E n T c ) = 0.09....
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MATH 352 HW3_solutions - (i No events A and B are not...

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