Mansoor50 wrote:
Hi.
the problem i have with these questions is as follows:
when it says 'randomly pick' .. does this mean we are picking WITHOUT looking? meaning i put my hand into the drawer and pick one - in which case i do not know which color i will get
OR
am i allowed to pick any color i want...in which case, its not random?
all the answers are deliberately picking one sock of each color....is that random?
help will be greatly appreciated
Hi Mansoor50.
You ask a great question.
While everyone has answered in the same way, the choosing of the socks is indeed random.
The question asks us how many socks have to be chosen at random in order for us to be SURE that we chosen at least two socks of the same color.
So, consider the following.
We could choose two socks at random and get two socks of the same color. But if we were to choose only two socks at random, would we be sure to get two socks of the same color? Since there are three colors of socks in the drawer, we could draw two socks of two different colors. So, by drawing only two socks at random, we wouldn't be sure to get two of the same color.
What if we were to randomly draw three socks? We might get two socks of the same color, or even three socks of the same color, but since there are three different colors of socks, we might draw one of each. So, if we were to draw three socks at random, we wouldn't be sure to get two socks of the same color.
Now, what if we were to draw four socks? Well there are only three different colors. So, after the first three, we know that we would definitely have run out of colors. So, even none of the first three were to match, the fourth one would have to match one of the first three.
So, by drawing four socks at random, we can be sure that we will draw at least two of the same color. We may have drawn one pair and two singles. We may have drawn two pairs. In any case, we will definitely have drawn two that match.
The correct answer is A.