A box has 60 balls, of which 22 are red, 19 are blue, and 19 are yellow, as before. Balls are extracted at random but this time not returned to the box. What is the probability that after performing this test three times exactly two are blue and one is red?

- anonymous

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- anonymous

when i do the calculation i got the answer 1818/17110 but the book answer have 5643/17110, i think i did something wrong my calculation

- anonymous

this what i did to get the calculation \[\frac{ \left(\begin{matrix}19 \\ 2\end{matrix}\right)* \left(\begin{matrix}22 \\ 1\end{matrix}\right)*\left(\begin{matrix}19 \\ 0\end{matrix}\right)}{ \left(\begin{matrix}60 \\ 3\end{matrix}\right)}\]

- amistre64

what is the test being performed?

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## More answers

- anonymous

combination

- amistre64

What is the probability that after performing ***this test*** three times exactly two are blue and one is red?
the questions feels like its missing information ... prolly from a different question?

- anonymous

k
A box has 50 balls, of which 16 are red, 19 are blue, and 15 are yellow. Balls are extracted at random then returned to the box. What is the probability that after performing this test three times exactly two are yellow and one is blue?

- anonymous

similar but a bit different w/ a number

- amistre64

experiment ... might be a better word

- anonymous

i see

- amistre64

A box has 60 balls, of which 22 are red, 19 are blue, and 19 are yellow, as before. Balls are extracted at random but this time not returned to the box.
What is the probability that after performing this (process) three times exactly two are blue and one is red?
rbb
brb
bbr
3*(22.19.18)/(60.59.58)
maybe?

- anonymous

doing that the number will be large

- amistre64

1881/17110 is what that turns out to be

- amistre64

P(bbr) or P(brb) or P(rbb)
are the only ways we can pull 2bs and 1r in 3 pulls right?

- anonymous

correct

- amistre64

and after we pull them out the remaining amounts decrease by 1
22 for red, 19 and 18 for blues
and the ball count reduces 60,59,58 for the product of the denominator ...

- anonymous

is like this |dw:1444575916412:dw|

- amistre64

not factorial,
3 * (22 P 1) * (19 P 2)
-------------------
(60 P 3)

- amistre64

but my solution is even less than yours, so i might not have a grasp of the information

- anonymous

i wonder what is p1 and p2 p3 use for ?

- amistre64

nPk is the permuations of n objects, k times it is used when the order matters
abc not equal bac
nCk is the combinations of n objects, k times it is used when the order doesnt matter
abc = bac
k! nCk = nPk

- anonymous

we are using the permutation instead of combination

- amistre64

yes, or at least as a basis for a model

- amistre64

there are 3 ways to pull bbr
and each pull has a probability of (22*19*18)/(60*50*58)

- amistre64

this is assuming it means that we are pulling 3 balls starting at the first pull.

- amistre64

59, not 50 ... my fingers hate me

- anonymous

k i see the answer |dw:1444576774278:dw|

- amistre64

1881 is what i get for a numerator
5643 is what your book gives, which is 3 times bigger than my outcome.
3*3*(...) where are they coming up with 9 different ways to order it?

- amistre64

what does "this test" refer to?

- anonymous

i have 3*(7524/205320)

- amistre64

which reduces yes

- anonymous

as you said the experiment

- amistre64

that was my assumption, but my outcome differs from the books outcome.
someones got to be wrong, and I assume its me :)

- amistre64

are you looking at the correct solution?

- anonymous

yes im

- anonymous

just said about the multi-step process

- amistre64

even your approach gets the same results as me

##### 1 Attachment

- TuringTest

I get the same answer as you guys. I am suspicious of the book's answer.

- amistre64

could it be possible that we are drawing more than 3 of them out for our sample space?

- anonymous

here the answer but do not show the step

##### 1 Attachment

- amistre64

3*(15*15*19)/(60*60*60) = 513/5000 so its the same approach

- amistre64

the book solution is wrong then

- anonymous

thank you so much for the correcting the confusion

- amistre64

im trying to see how they could have gotten an answer 3 times bigger, but other than a simpler human error in inputing it to begin with i cant duplicate it.

- anonymous

k

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