Chapter 1.1, Problem 4E

A fair coin is tossed four times, and the sequence of heads and tails is observed.

(a) List each of the 16 sequences in the sample space S.

(b) Let events A, B, C, and D be given by $\text{A }=\left(\text{at least 3 heads}\right),\text{ B }=\left(\text{at most 2 heads}\right),$ $\text{C }=\left(\text{heads on the third toss}\right),$ and $\text{D }=\left(\text{1 head and 3 tails}\right)$.

If the probability set function assigns 1/16 to each outcome in the sample space. find (I) $P\left(A\right)$, (ii) $P\left(A\cap B\right)$, (iii) P(B), (iv) $P\left(A\cap C\right)$, (v) P(D), (vi) $P\left(A\cup C\right)$, and (vii) $P\left(B\cap D\right)$.