There is a large jar of marbles, containing red, blue, yellow, black and white marbles. How many marbles must you draw(without looking) from the jar to be sure of getting at least three of one color?
I have a similar question with socks:
10 white, 6 black, how many drawn for one pair of white socks?
I will do the socks one ...
number of possible pairs = C(16,2) = 120
number of possible white pairs = C(10,2) = 45
so prob that both are white = 45/120 = 3/8
3 : 8 = 1 : 2.6667
Unless my thinking is way off, appr every third pair (I rounded it off) chosen would be a white pair.
To determine how many marbles or socks you must draw to be sure of getting at least three of one color, you need to consider the worst-case scenario.
For the marbles, let's assume the jar contains equal quantities of each color. The worst-case scenario would be if you draw two marbles of each color (a total of 10 marbles). In this case, you would have two marbles of each color but still not three marbles of any specific color. To guarantee getting at least three marbles of one color, you would need to draw one more marble. Therefore, you must draw a minimum of 11 marbles.
Now, let's consider the socks. To determine the minimum number of socks you must draw to be sure of getting one pair of white socks, you need to consider the worst-case scenario. Since you have 10 white socks and 6 black socks, the worst-case scenario would be if you draw all the black socks before finding a pair of white socks. In this case, you would need to draw a total of 7 socks to guarantee obtaining one pair of white socks.
Remember that these calculations assume the worst-case scenario and may not reflect the actual number of marbles or socks you need to draw in most cases.