Prof gave us homework on conditional probability that is due on the day of the lecture on conditional probability. Yeah, this has been a bad week and I've no idea what I'm doing.
Q: 3 dice are rolled, then, a coin is flipped as many times as the number 6 is obtained.
a) find the probability of getting less than 2 heads.
b) knowing this experiment results in less than 2 heads, what is the conditional probability that exactly 2 sixes were obtained?
I don't even know where to start...
Attempt:
a)
The only way I figure is:
Rolling one six, probability of head < 2 = $ \displaystyle \frac{3}{6^3} \cdot \frac{2}{2}$
Rolling two sixes: $\displaystyle \frac{3}{6^3} \cdot \frac{2}{2^2}$
Rolling three sixes: $\displaystyle \frac{1}{6^3} \cdot \frac{4}{2^3}$
Then adding those.
b)
$\displaystyle \frac{\frac{1}{6^3} \cdot \frac{4}{2^3}}{\frac{1}{6^3}}$