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?

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- Jul 31st 2008, 10:16 AMkas34probability
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? - Jul 31st 2008, 10:47 AMarbolisQuote:

roll a die 3 times. what is the probability of getting at least two 6's?

Quote:

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. - Jul 31st 2008, 10:55 AMjanvdl
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:

$\displaystyle {3 \choose 2} \left( \frac{3}{6} \right) ^{2} \left( \frac{3}{6} \right) ^{1} + {3 \choose 3} \left( \frac{3}{6} \right) ^{3} \left( \frac{3}{6} \right) ^{0}$ - Jul 31st 2008, 11:00 AMPn0yS0ld13r
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

$\displaystyle \displaystyle\sum_{r=1}^{3}\dbinom{3}{r}\left( \frac{1}{2} \right) ^{r} \left ( \frac{1}{2} \right) ^{3-r} = \frac{7}{8}$ - Jul 31st 2008, 11:01 AMjanvdl
- Jul 31st 2008, 11:07 AMarbolis
kas34, don't mind my answer, I didn't realize there were 3 pitches.

- Jul 31st 2008, 11:09 AMjanvdl