If you have black socks and brown socks in your drawer, mixed in a ratio of 4 to 5, how many socks will you have to take out to make sure that you have a pair the same color?

Maximum 3 socks (minimum 2) to be taken out to have a pair of same color.

Step-by-step explanation:

Well, it can be assumed that for example there are 4n black and 5n brown socks in a drawer (which satisfies ratio of 4/5). If first sock is taken out the probability of this sock being black is 4/9 (4n/(4n+5n)) or being brown is 5/9 (5n/(4n+5n)). If the first sock is black, the probability of second attempt being black is (4n-1)/(9n-1), but being brown is (5n)/(9n-1). f the first sock is brown, the probability of second attempt being brown is (5n-1)/(9n-1), but being black is (4n)/(9n-1). In either case, there is a probability of taking out different colors of socks in two attempts (taking black first then brown or vice-versa). So maximum 3 (minimum 2) attempts required to make sure you have a pair of the same color of socks.

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation:

step-by-step explanation: