Sheldon Ross Introductory Statistics - Probability Section 4

Have been supplementing this with Khan Academy's probability lectures - they do a good job of starting from basics (needed for someone like me who last did math in school - 15 years back) and deriving the concepts from scratch. At some point I do have to read Bertsekas and follow/work through MIT's lectures.

Ch 4 Problems

1.
(a) S = {(R,R),(R,B),(R,Y),(B,B),(B,R),(B,Y),(Y,Y),(Y, R),(Y,B)}
(b) S = {(Y,Y),(Y, R),(Y,B)}
(b) S = {(R,R),(B,B),(Y,Y)}

2.
(a) S = {(R,B),(R,Y),(B,R),(B,Y),((Y, R),(Y,B)}
(b) S = {(Y, R),(Y,B)}
(c) S = {}

4.
(a) S = {(H, H, H),(H, H, T),(H, T, T),(T,T, T),(T , T, H),(T, H, T),(H, T, H), (T, H,H) }
(b) S = {(H, T, T),(T,T, T),(T , T, H),(T, H, T)}

5.
S = {(F, boat), (F, fly), (C, drive), (C, train), (C, fly)}
A = {( (F, fly), (C, fly)}

7.

(a) A ∪ B = Φ
(b) B ∪ C = {1,4,6}
(c) A ∪ (B ∩ C) = {1,3,4,5}
(d) (A ∪ B) c = {2}

8.
(a) S = {(C, P, IC), (C, P, G), (C, P, AP), (RB, P, IC), (RB, P, G), (RB, P, AP),
(C, R, IC), (C, R, G), (C, R, AP), (RB, R, IC), (RB, R, G), (RB, R, AP),
(C, Po, IC), (C, Po, G), (C, Po, AP), (RB, Po, IC), (RB, Po, G), (RB, Po, AP)}

(b) A = {(C, P, IC), (RB, P, IC), (C, R, IC), (RB, R, IC), (C, Po, IC), (RB, Po, IC)}

(c) B = {(C, P, IC), (C, P, G), (C, P, AP), (C, R, IC), (C, R, G), (C, R, AP), (C, Po, IC), (C, Po, G), (C, Po, AP) }

(d) A ∩ B = {(C, P, IC), (C, R, IC), (C, Po, IC) }

(e) C = {(C, R, IC), (C, R, G), (C, R, AP), (RB, R, IC), (RB, R, G), (RB, R, AP) }

(f) A ∩ B ∩ C = {(C, R, IC) }

10.
(a) Yes
(b) Yes
(c) No
(d) No
(e) Yes

11.
(a) Die lands on an odd number
(b) Die lands on an even number
(c) The event itself

12.

(a) Second dice lands on 1, 3, 5
(b) A ∪ B = A
(c) Second dice lands on 5
(d) First dice lands on 2,3,4,5,6
(e) Sum of dice is odd ∩ sum of dice is 6 = Ø
(f) Event = {(5,1),(3,3),(5, 1)}