1. The following is the three coins toss sample space, $S=\{T IT, I TH, THI, THH, HIT, HTH, HHT, H H H\}$ Define the following event as a subset of sample space $5$. (a) $A$ : the second toss results in a tail (b) $B$ : a head comes before a tail (c) $C: $ an event that third toss is a head but no information about the outcome of the first two tosses (d) D: Assuming the equal probability of two outcomes for the coin toss, i.e., $P(H)=P(T)=0.5$, what are $P(A), P(B)$, and $P(C)$ ? (e) $E$ : if $P (H)=0.4$ and $P(T)=0.6$, what are $P(A), P(B)$, and $P(C) ?$ SP.VS.8971