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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)

$\displaystyle \frac{\frac{1}{6^3} \cdot \frac{4}{2^3}}{\frac{1}{6^3}}$

2 Answers 2