Probability

I have a probability question.
? I roll a six sided dice 6 times. What is the probability that I will roll exactly three sixes?

I am using the P(E)= # of times event (E) has occured / total number of times the experiment has been performed

so to me...it should be 3/6, but i need the answer to be in decimal form. But I am not even sure I am using the right kind of equation to find the answer.
Thanks for your help!

Cheryl

mamagreeneyes said:

I have a probability question.
? I roll a six sided dice 6 times. What is the probability that I will roll exactly three sixes?

Click to expand...

\(\displaystyle \binom{6}{3}\left(\frac{1}{6}\right)^3\left(\frac{5}{6}\right)^3\)
WHY?

The book is asking for a answer that is a decimal.
I even tried doing it like this:
1/6(1) + 1/6(2) + 1/6(3) + 1/6(4) +1/6(5) + 1/6(6)
.17 + .33 + .5 + .67 + .83 + 1



This is in a study manual I am working through. The only answers I have are 4 possible choices. They are all decimals.
It has been a while since I have done college math, and I am finding it hard to grasp at times.
Thank you for your help though....

pka said:

\(\displaystyle \binom{6}{3}\left(\frac{1}{6}\right)^3\left(\frac{5}{6}\right)^3\)

Click to expand...

You seem more interested in turning something into decimals than "learning" how the
probability calculation works...anyhoo:
pka's left expression means "6 choose 3" : that's 20
If you want to see how that works, go here:
http://www.google.ca/search?hl=en&q=6+c ... =&aq=f&oq=

So we have 20 * (1 / 216) * (125 / 216) ; multiply that out:
2500 / 46656; now do the division:
.053583676... there's your dearly loved decimal :wink:

So (rounded) probability is .05 (or 5%; 1 in 20) ; you ok with that, GreenEyes?

Well, that explaination helped. Thanks! And thank you for the link. I am going to go there now.....