Question

Dear all,
I have a little problem with the following statement:
A box contains 8 pieces each of milk chocolate, white chocolate, and dark chocolate. The box is passed around the six of us, with each person taking 4 pieces. Assume that each person chooses at random without replacement from the available pieces. I am the last person to whom the box is passed. Find the chance that I pick 4 dark chocolates.

Please help me! Thank you in advance.

Answer 1

1/3*1/3*1/3*1/3

Answer 2

so 1/81
a one in 81 chance that you will pick our 4 consecutive dark chocolates

Answer 3

I checked it; it is not correct. Don't you think that you have to take intov consideration the fact that you are the last one and they the friends before you can't pick all the dark chocolates ?

Answer 4

if everyone's picking at random then it doesnt affect the probability and they could easily have taken all of the dark chocolates

Answer 5

your initial probability is 1/3 as you have 8 white, 8 milk and 8 dark in the box

Answer 6

maybe im wrong though, thats just how i read it

Answer 7

is the answer 1/10626?

Answer 8

No, how did you get to that answer?

Answer 9

You can think the problem as follow: Take out 4 dark chocolates from the 24 chocolates, these are reserved for you. The rest 20 chocolates are now be distributed among 5 people, which can be done in 20!/(4!)^5. Now the total number of ways to distribute 24 chocolates among 6 people is 24!(4!)^6. Divide them. Anyway not the correct answer though.

Answer 10

1/1296 is what i get?
here's how i think of it, taking whatever is last is the same as picking first in the maths. So chances of picking 4 dark in a row out of 24 chocolates is (4/24)^4 = 1/1296

Answer 11

no, not that way, it's done WITHOUT replacement.

Answer 12

if order is not taken into account, then we'll have 1/1771. I'm pretty sure about my argument, just don't know my answer is wrong.

Answer 13

8/24*7/23*6/22*5/21; is this correct?

Answer 14

there's 24 pieces of chocolate if there's 8 white 8 chocolate and 8 dark

Answer 15

all 24 picks are accountable since there's 6 of you and each person takes 4

Answer 16

I'm not in statistics, but this is what I think...assuming that three people aren't big fans of dark chocolate, you may get a chance but it's slim to none

Answer 17

From 8 white, choose 8, from 8 milk, choose 8, and from 8 dark, choose 4 (leaving 4). Divide by the total number of ways to choose 20 chocolates from 24.

\[\large \frac{ 8 C 8 \times 8 C 8 \times 8 C 4 }{ 24 C 20} = \frac{ 70 }{ 10626 }\]

Answer 18

8/24*7/23*6/22*5/21

Answer 19

Note that it doesn't matter how many people picked before you, just that 20 chocolates have been picked, and 4 remain.

Answer 20

@abhi_abhi's answer works too.