I have a drawer which contains 40 socks in the following numbers and colors: 12 tan, 9 brown, 11 gray, and 8 blue. Suppose I am blindfolded. What is the fewest number of socks I must pick from the drawer to be absolutely certain that I have two socks of the same color among those I have picked?
Thanks, Ms. Sue
Please can you explain? I've lot of trouble with probability.....
If you draw 4 socks, you could get one of each color. The fifth sock has to match at least one of the socks that you drew.
If you have trouble visualizing this, try it with socks, or playing cards, or colored paper, or M & Ms.
issa 5
obviously 5
To find the fewest number of socks you must pick from the drawer to be absolutely certain that you have two socks of the same color, you can use the concept of the Pigeonhole Principle.
The Pigeonhole Principle states that if there are more pigeons (or socks, in this case) than pigeonholes (or colors), at least one pigeonhole must contain more than one pigeon.
In this case, you have 40 socks with 4 different colors. To be absolutely certain that you have two socks of the same color, you need to consider the worst-case scenario. In the worst-case scenario, you would pick one sock of each color successively. This means that you would need to pick 4 socks to cover all the colors.
Therefore, the fewest number of socks you must pick from the drawer to be absolutely certain that you have two socks of the same color is 4 socks.
Math - Ms. Sue, Thursday, February 27, 2014 at 3:39pm Answer is correct so the
No of draw is 5 ..
Answer 5.