Answer:
P(A) = 0.4 ; P(B) = 0.50 ; P(C) = 0.60 ; P(A u B) = 0.65 ; P(A n B) = 0.25 ;
A and C are mutually exclusive ;
0.5
Step-by-step explanation:
S = {E1, E2, E3, E4, E5, E6, E7}
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}
P(A) = 0.05 + 0.25 + 0.10 = 0.40
P(B) = 0.20 + 0.25 + 0.05 = 0.50
P(C) = 0.20 + 0.20 + 0.15 + 0.05 = 0.60
AUB = {E1, E2, E4, E6, E7}
P(A u B) = 0.05 + 0.20 + 0.25 + 0.10 + 0.05 = 0.65
AnB = {E4}
P(A n B) = 0.25
A and C are mutually exclusive if AnC = ∅
A n C = ∅
Hence, A and C are mutually exclusive.
B complement = B' = {E1, E3, E5, E6}
P(B') = 0.05 + 0.20 + 0.15 + 0.10 = 0.5
