Question

Toss a coin 3 times. Let x be product of (# of H)*(# of T). Find
1. P(X>1)=
2. Var(X)=

Answer 1

After 3 tosses, you can have HHH, HHT, HTH, THH, HTT, THT, TTH, or TTT (8 outcomes).

Now list your products. E.g. For HHH:
(#H)(#T) = (3)(0) =0
Work out the rest of the products, and put how many are > 1 over 8.

This is a binomial distribution, so:
Var(X) = np(1-p)