Suppose that we have a sample space S = {E_1, E_2, E_3, E_4, E_5, E_6, E_7}, whe

Question

Suppose that we have a sample space S = {E_1, E_2, E_3, E_4, E_5, E_6, E_7}, where E_1, E_2,..., E_7 denote the sample points. The following probability assignments apply: P(E_1) = 0.05, P(E_2) = 0.15, P(E_3) = 0.1, P(E_4) = 0.25, P(E_5) = 0.15, P(E_6) = 0.1, and P(E_7) = 0.2. Assume the following events when answering the questions. A = {E_1, E_4, E_6} B= {E_2, E_4, E_7} C = {E_2, E_3, E_5, E_7} a. Find P(A), P(B), and P(C). P(A) P(B) P(C) b. What is P(A 8)? c. What is P(A B)? d. Are events A and C mutually exclusive? e. What is P(B^C)?.

Explanation / Answer

A. A={E1,E4,E6}

P(A)= probability of occuring e1,e4 and e6

=P(E1)*P(E4)*p(E6)=0.05*0.25*0.1=0.00125

P(B)=probability of occuring e2,e4 and e7=P(e2)*P(e4)*P(e7)=0.15*0.25*0.2=0.0075

P(C)=probability of occuring e2,e3,e5 and e7=P(E2)*P(E3)*p(E5)*P(E7)=0.15*0.1*0.15*0.2=0.00045

B.P(AuB)=P(A).P(B)=0.00125*0.0075=0.00000938

C.P(A not B)=1-P(AuB)=1-0.00000938=0.99999062

D. Mutually exclusive is event that can't happen at the same time. They have different set of events which cannot happen same time hence they are mutally exculsive as S=combination of both A and C without repition of any event.

E.P(b|c)=P(b and C)/P(C) which is P(B) when C has occured=P(B)*P(C)/.P(C)=P(B)=0.00000938

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