8 i think 8 i think I guess it's 6.. and my point is that you have to try it through the worst sequence ever. starting with the red one (the one that is impossible for you to get another one, and will never reach the three same colored wanted) then start getting one of each of the two other colors each time, alternating, so it will take longer for you to have several of the same color: example: red > black > white > black > white > black (3 black ones)
or red > white > black > white > black > white (3 white ones) or (just to prove that alternate sequence isn't needed) white > black > black > red > white > (...)
(impossible to get any marble without getting the third of it's color, and by not getting the red one, this would have been impossible to reach, so to be SURE, you have to count this one in the first five, or it would come or not in the 5th position)
in this case, a longer sequence would have got the three equal-colored marbles some time ago. remembering, that this sequence is just to explain that 6 would do the job, and these balls would have been caught in a handful of marbles =) ps.:sorry for my poor English.
You would need to take out at least 5 marbles to ensure you have 3 of the same color. This is because in the worst-case scenario, you could end up with 2 marbles of each color after drawing 4 marbles (2 white, 2 black) and adding 1 more marble guarantees that you will have at least 3 of one color.
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The theoretical probability of randomly picking each color marble is the number of color marbles you have for each color, divided by the total number of marbles. For example, the probability of selecting a red marble is 3/20.
a black one
The maximum number of marbles you have to draw is three. 1) Draw a marble. It is either white or black. 2) Draw a second marble. If it is the same colour as the first marble, we are done after two draws. 3) Otherwise, the drawn marbles have different colours. Draw a third marble. No matter what you draw next, you must have two marbles of the same colour.
== ==
3/6 or 1/2 or 50%
Number of possibilities for one category / Total of all possibilities. For example, if I had a bag of marbles where there are three white marbles and two black marbles. The probability of pulling out a white marble is how many white marbles are in the bag which is: three. But the total of things you can draw out of the bag can either be one of the three white marbles or one of the two black marbles. 3 white marbles+ 2 Black marbles= five marbles. Possibility is 3/5 for drawing a white marble.
3/6 * 3/5 = 6/30 or 1/5 so you have a 20% chance of pulling a white and then black marble.
The probability of drawing a white marble is .46
3/7*3/7= 9/49
80% chance, Or 40/50
1 in 1024 :-)
1 in 52