my question is: roll a die 3 times. what is the probability of getting at least two 6's?
also: what is the probability of not getting any even number?
When you pitch one dice, the probability to get a $\displaystyle 6$ is $\displaystyle \frac{1}{6}$. If you pitch it twice, it will be $\displaystyle \frac{1}{6} \cdot \frac{1}{6}=\frac{1}{36}$.roll a die 3 times. what is the probability of getting at least two 6's?
When you pitch one dice, the probability to not get an even number is $\displaystyle \frac{1}{2}$. So when you pitch it twice, the probability to not get any even number is $\displaystyle \frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$.what is the probability of not getting any even number?
To understand why it is so, you have to know that the probability of an event is equal to the number of favorable events divided by the number of possible events. For example when I said that you have a probability of $\displaystyle \frac{1}{2}$ of not getting an even number when you pitch one dice, using the formula we have $\displaystyle \frac{3}{6}=\frac{1}{2}$. 3 over 6 because the favorable outcomes are 1,3 and 5. And the possible outcomes are 1,2,3,4,5 and 6.
Use the binomial probability for both these:
Probability for at least two 6's when rolled 3 times:
$\displaystyle {3 \choose 2} \left( \frac{1}{6} \right) ^{2} \left( \frac{5}{6} \right) ^{1} + {3 \choose 3} \left( \frac{1}{6} \right) ^{3} \left( \frac{5}{6} \right) ^{0}$
Not getting any even number for at least 2 out of 3 throws:
$\displaystyle {3 \choose 2} \left( \frac{3}{6} \right) ^{2} \left( \frac{3}{6} \right) ^{1} + {3 \choose 3} \left( \frac{3}{6} \right) ^{3} \left( \frac{3}{6} \right) ^{0}$
Actually, I think the answer is $\displaystyle \frac{7}{8}$ because the question asks what is the probability of getting AT LEAST two 6's.
Consider using binomial distribution, Binomial Distribution -- from Wolfram MathWorld
$\displaystyle \displaystyle\sum_{r=1}^{3}\dbinom{3}{r}\left( \frac{1}{2} \right) ^{r} \left ( \frac{1}{2} \right) ^{3-r} = \frac{7}{8}$