Question

okay last time I'm going to ask this...a die is rolled 5 times. find the probability p(of exactly 3 occurrences of 6)
a. 1.86%
b. 2.08%
c. 2.23%
d. 3.22%

Answer 1

Do you know the formula for Bernoulli trials?
http://en.wikipedia.org/wiki/Bernoulli_trial

Answer 2

no:(...i've tried to make sense of it but its just not processing

Answer 3

The event of interest is rolling a 6
What is the probability (in a single roll)

Answer 4

The probability of rolling a 6 is 1/6 (six-sided dice)
Call that p
The probabiliity of not rolling a 6 is (1-p)
What do you think n and k stand for in the formula?

Answer 5

is bernie the same as a binomial distribution?

Answer 6

i think formulas are overrated

Answer 7

formula one racers would disagree :)

Answer 8

the probability you roll a six on one die is \(\frac{1}{6}\) and the probability you do not roll a six is therefore \(\frac{5}{6}\)

Answer 9

but maybe not nascar drivers

Answer 10

they got nascar in the olympics yet?

Answer 11

@amistre64 Yes

Answer 12

That's the way they index it in Wikipedia

Answer 13

.... yes bernie is binomial; yes formula one racers disagree; or, yes nascar is in the plympics? :)

Answer 14

multiple choice!
A

Answer 15

in any event, since the rolling of a die many times is an example of independent events (the dice have no memory) then what do you want? 3 sixes and 2 not sixes
since the events are independent, you multiply the probabilities together to get
\[(\frac{1}{6})^3\times (\frac{5}{6})^2\] which would give you the probability of rolling 3 sixes in a row and ten two not sixes
but you do not need them to be in a row, you just need 3 sixes and 2 not sixes
the number of way to choose 2 out of 5 (or 3 out of 5) is \(\dbinom{5}{2}=\frac{5\times 4}{2}=10\)

Answer 16

@satellite73 Thanks for working through it for him.

Answer 17

I just get a little discouraged when there is not any help from the OP.

Answer 18

and so your answer would be
\[20\times \left(\frac{1}{6}\right)^3\times \left(\frac{5}{6}\right)^2\]
which is what the formula tells you, but also what you get by thinking

Answer 19

thanks:)

Answer 20

then a calculator would be helpful
hope all the steps are clear, and more importantly that the formula
\[P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}\] makes some sense
do not get married to the formula, make sure to understand what it really says