7)
P(X = k) = nCk p^k * (1-p)^(n-k)
a)
sample space = {HHHH,HHHT,...TTTT}
size = 2^4 = 16
b)
i) P(A)
number of times there are at least 3 heads = 4C3 + 4C4 = 4 +1 =
5
hence
P(A) = 5/16
ii)
P(A and B)
= 0 {both A and B can't be true at any instance}
iii)
P(B) =
4C0 + 4C1 + 4C2 = 1 + 4 + 6 = 11
hence 11/16
iv)
P(A and C)
= P(heads on 3rd toss) and P(at least 2 heads in remaing 3
toss)
= 1/2 * (3C2 + 3C1)/2^3
= 1/2 * 4/8
=1/4
Please post rest questions again
7-10 help 0.4, P(B)0.5, and P(A UB)-0.7, find P(An B) P(A' U B') 6. If P(A)...
Help 8-10 0.4, P(B)0.5, and P(A UB)-0.7, find P(An B) P(A' U B') 6. If P(A) a. b. 7. A coin is tossed 4 times and the sequence of heads and tails is observed a. b. What is the sample space S for this experiment? Consider the following events: A [at least 3 heads) B- (at most 2 heads) C- (heads on the 3rd toss) D - [1 head and 3 tails) If the outcomes in S are equally likely,...
6-10 help 6. If P(A) 0.4, P(B) 0.5, and P(A UB) 0.7, find a. P(A n B) b. P(A' U B') 7. A coin is tossed 4 times and the sequence of heads and tails is observed a. b. What is the sample space S for this experiment? Consider the following events: A [at least 3 heads) B- (at most 2 heads) C = {heads on the 3rd toss) D- (1 head and 3 tails) If the outcomes in S...
8-10 0.4, P(B)0.5, and P(A UB)-0.7, find P(An B) P(A' U B') 6. If P(A) a. b. 7. A coin is tossed 4 times and the sequence of heads and tails is observed a. b. What is the sample space S for this experiment? Consider the following events: A [at least 3 heads) B- (at most 2 heads) C- (heads on the 3rd toss) D - [1 head and 3 tails) If the outcomes in S are equally likely, find...
Question 5 (1 point) <Venn 6> There are 2 events: A, B with P(A)-0.5, P(B)-0.4, P(AUB)=0.7 Find P(Ac UB) (2 decimal places without rounding-up) Question 6 (1 point) Saved There are 2 events: A, B with P(A)-0.5, P(B)-0.4, PAUB)-0.7 Find P(A B)
#24,28,32 In Exercises 17-40, let (1,2,3, 4,5, 6, 7) 11,3,5,7) U A C (2,3,4, 5,6). Find each of the following sets 17. AnB 20. BU C 23, A,NB, 26. BUC 29. A'U C 32. (AUC)' 35. AnØ 38. BU U 18. ВПС 21. A 24. в'nc 27. (AnC) 30. A' U B' 33. AU0 36. CnØ 39. AnU 19. A U B 22. B' 25. AUC 28. (An B)' 31. (A U B)' 34. CUØ 37. AU U 40. BnU
2.16 Suppose that P(A) = 0.4, P(B) = 0.5 and P(AB) = 0.2. Find the following: a) P(AUB) b) P(A'B) e) PIA'(AUB) d) PIAU(A'B)
2.40 Given that P(A)0.3, P(B) 0.5 and P(B|A)0.4, find the following a) P(AB) b) P(A|B) e) P(A'IB) d) P(AIB)
If P(E)=0.4, P(F) = 0.5, and P( E (a) P(E") (b) PEUF) F)=0.2, find the following (a) P(E") =D (Simplify your answer. Type an integer or a decimal.) (b) P(EU F)=0 (Simplify your answer. Type an integer or a decimal.)