Solution

a. Let 

$C$ and $S$ be the event that a 666 is selected in lottery at Connecticut and Pennsylvania. The lotteries in Connecticut and Pennsylvania are independent. Thus, $P(C|S)= P(C)$.

The total possible number of 3 digit combinations is $10 \times 10 \times 10= 1000$ and each of them is equally likely to be selected. This gives probability that a 666 would be drawn in Connecticut, $P(C)$ as $\dfrac{1}{1000}.$

Answer

a. $\dfrac{1}{1000}$

b. $\dfrac{1}{8000}$