Independent and Mutually Exclusive Events: example 3.7

Look at the sample space in Example 3.6.

1. Zero (0) or one (1) tails occur when the outcomes HH, TH, HT show up. P(F) = $\frac{3}{4}\text{.}$
2. Two faces are the same if HH or TT show up. P(G) = $\frac{2}{4}\text{.}$
3. A head on the first flip followed by a head or tail on the second flip occurs when HH or HT show up.
   P(H) = $\frac{2}{4}\text{.}$
4. F and G share HH so P(F AND G) is not equal to zero (0). F and G are not mutually exclusive.
5. Getting all tails occurs when tails shows up on both coins (TT). H’s outcomes are HH and HT.

J and H have nothing in common so P(J AND H) = 0. J and H are mutually exclusive.