A sample space consists of 9 elementary events E1, E2, E3, ..., E9 whose probabilities are
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
Suppose A = {E1, E5, E8}, B = {E2, E5, E8, E9}
Calculate \[P\left( \bar{ B} \right)\] from P(B), also calculate \[P\left( \bar{ B } \right)\] directly from the elementary events of \[\bar{ B } \] .
Solution
Let S be the sample space of the elementary events.
S = {E1, E2, E3, ..., E9}
Given:
A = {E1, E5, E8}
B = {E2, E5, E8, E9}
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
\[P\left( B \right) = 1 - P\left( B \right) = 1 - 0 . 32 = 0 . 68\] [From (i)]
Also, we know that \[\bar{ B } \]= S − B = {E1, E3, E4, E6, E7}
∴ \[P\left( \bar{B} \right)\] = P(E1) + P(E3) + P(E4) + P(E6) + P(E7)
= 0.08 + 0.1 + 0.1 + 0.2 + 0.2
= 0.68
Notes
The solution of the problem is provided by taking P(E5) = 0.1. This information is missing in the question as given in the book.
