Suppose that we have a sample space S={E1, E2, E3, E4, E5} where P(E1)=0.2, P(E2)=0.28, P(E3)=0.12, P(E4)=0.18, and P(E5)=0.22.
Let A={E1, E3, E5},
B={E3, E4},
C={E1, E4, E5}.
Are events C and B independent?
Suppose that we have a sample space S={E1, E2, E3, E4, E5} where P(E1)=0.2, P(E2)=0.28, P(E3)=0.12,...
suppose that we have a sample space s={E1,E2,E3,E4,E5,E6,E7}, where E1 to E7 denote the sample points. The following probability assignments apply: p(E1 )=.05 p(E2)=.20 P(E3)=.20 p(E4)=.25 p(E5)=.15 p(E6)=.10 and p(E7)=.05 Let A={E1,E4,E6} B={E2,E4,E7} C= {E2,E3,E5,E7} 1) Find A ∩ B and P(A ∩ B) and Are events A and C mutually exclusive?
Suppose a sample space consists of five elementary outcomes e1, e2, e3, e4, e5with the characteristics that e1, e4, and e5are equally likely, e2is twice as likely ase1and e3is four times as likely as e1. a. DetermineP(ei) for i = 1, 2, ... 5 b. IfA = {e3, e4}, find P( A ).
Suppose that we have a sample space with seven equally likely experimental outcomes: E1, E2, Es, EA, E5, E, and E. Let a. Find P(A), P(B), and P(C) (to 2 decimals). P(A)29 P(B)29 P(C) 43 b. Find P(AU B) (to 2 decimals). b. Find P(AUB) (to 2 decimals) Are A and B mutually exclusive? -Select your answer- c. Find Ac, Ce, P(A), and P Ce) A -Select your answer- -Select your answer- (to 2 decimals) (to 2 decimals) d. Find...
F is an event, and E1, E2, and E3 partition S. P(E1) = 5 12 , P(E2) = 4 12 , P(E3) = 3 12 P(F | E1) = 2 5 , P(F | E2) = 1 4 , P(F | E3) = 1 3 Draw the tree diagram that represents the given information. (a) Find P(E1 ∩ F), P(E2 ∩ F), P(E3 ∩ F). P(E1 ∩ F) = P(E2 ∩ F) = P(E3 ∩ F) = (b) Find P(F). P(F) =...
We have two events (E1 and E2) that are independent. If P(E2 given E1) is 0.8, what is P(E2)?
A chance experiment consists of drawing a raffle ticket from a box of tickets numbered 1, · · · , 40. Let Ω represent the sample space for this experiment. Since we select one ticket at random, Ω is an equally-likely sample space. Let E1,··· ,E8 where Ei ⊂ Ω be a partition of Ω defined as: E1 = {1,3,5,7,9}, E2 = {11,13,15,17,19}, E3 = {21,23,25,27,29}, E4 = {31,33,35,37,39}, E5 = {2,4,6,8}, E6 = {10,12,14,16,18}, E7 = {20,22,24,26,28}, E8 =...
Let E and F be two events of an experiment with sample space S. Suppose P(E)= 0.4, P(F)=0.3, P(E U F) =0.5, Find P(F|E) and determine if the two events are independent. A) P(F|E)= 3/4, E and F are independent. B) P(F|E)= 3/4, E and F are not independent. C) P(F|E)=1/2 , E and F are independent. D) P(F|E)= 1/2, E and F are not independent.
Let and B be events in a sample space S, and let C = S - (AUB). Suppose P(A) = 0.8, P(B) = 0.2, and P(An B) = 0.1. Find each of the following. (a) P(AUB) (b) P(C) (c) PAS (d) PLAC BC) (e) PLACUBS (1) P(BCnc)
Events A, B, and C in a sample space have P(A)=0.2, P(B)=0.4, P(C)=0.5, P(~B ∪ ~C)=0.9, and P(A ∪ C)=0.6. Find P(A ∪ B ∪ C) if A and B are mutually exclusive.
Suppose we have two events A and B. Suppose further that P(A) - 0.1, PB)-0.2, and P(AUB) = 0.3. a. [2 marks] Calculate P(A NB) b. [2 marks] Use the mathematical definition of independence to determine if A and B are independent. Conclude in a single sentence. Use only one of the two appropriate c. [2 marks] Use the mathematical definition of mutual exclusivity to determine if A and Bare mutually exclusive. Conclude in a single sentence. MacBook Air #58...