1.You have exactly 18 white socks and 18 blue socks in your sock drawer. How many times do you need to reach into the drawer and take out a sock to guarantee a matching pair?

3 times

Step-by-step explanation:

Given

18-white socks

18 blue socks

36 socks total

First time reached in,

18/36 ( =1/2=(50%)) chance of getting a white sock, 18/36 (=1/2=(50%)) chance of getting a blue sock

assuming you got a white sock,

17-white socks

18-blue socks

35 socks left in

Second time reached in,

17/35 (<1/2=(50%)) chance of getting a white sock, 18/35 (>1/2=(50%)) chance of getting a blue sock

You would be more likely to get a blue sock, assuming you did,

17-white socks

17-blue socks

34 socks left

Third time reached in,

17/34(=1/2=(50%)) chance of getting a white sock, 17/43(=1/2(50%)) chance of getting a blue sock

Regardless of what sock is picked you would have a matching pair of socks in hand

i can try and you the very best that i can.