Chapter 4.4, Problem 1E

Experiment I An experiment can result in one of fiveequally likely simple events, $E_1,E_2,\mathrm{....}{E}_5$. Events A,B, and C are defined as follows. Use these events toanswer the questions in Exercises 1−6.

$\begin{array}{l}A:E_1,E_{3}P\left(A\right)=.4\\ B:E_1,E_2,E_3,E_4,E_{5}P\left(B\right)=.8\\ C:E_3,E_{4}P\left(C\right)=.4\end{array}$

1. Find the probabilities associated with the followingevents by listing the simple events in each.

a. $A^c$      b. $A\cap B$    c. $B\cap C$
d. $A\cup B$    e. $B|C$    f. $A|B$
g. $A\cup B\cup C$     h. ${\left(A\cap B\right)}^c$