# You flip a coin and roll a die. What is the probability that you obtain a head on the coin and a 2 on the die?

Feb 12, 2015

The probability that you obtain a head on the coin and a 2 on the die is $\left(\frac{1}{2}\right) \cdot \left(\frac{1}{6}\right) = \left(\frac{1}{12}\right)$

Assuming the coin and the die are unbiased:
the probability of obtaining a head on the coin is $\frac{1}{2}$ (50%)
and
the probability of obtaining a 2 on die is $\frac{1}{6}$.

These are independent events. What happens with the coin does not effect what happens with the die.
Therefore the probability of the combined outcome is the product of their individual probabilities.

From the above we can see that there are 12 (6 X 2) possible combined outcomes.
The desired outcome (the intersection of the Die Outcome $= 2$ and the Coin Outcome $= H$) only occurs once.

Therefore the probability of the desired outcome is $1$ out of $12$ (or, $\frac{1}{12}$).