Chapter 8.3, Problem 49E

A fair coin is tossed twice. Consider the sample space $S=\left\{\text{HH,}\text{HT,}\text{TH,}\text{TT}\right\}$ of equally likely simple events. We are interested in the following events:

$E_1=$ a head on the first toss

$E_2=$ a tail on the first toss

$E_3=$ a tail on the second toss

$E_4=$ a head on the second toss

For each pair of events, discuss whether they are independent and whether they are mutually exclusive.

(A) $E_1$ and $E_4$

(B) $E_1$ and $E_2$