socks in a drawer probability
I need some help with the following problem:
You have 30 socks in a drawer, 10 red, 16 black and 4 blue. You are
removing socks from the drawer in the dark, so you cannot see the colours. How many socks do you need to take out to be certain you have:
(a) A matching pair of socks.
(b) Two matching pairs of socks.
(c) Two matching pairs of different colours.
(d) Two blue socks.
(a) The socks come in three possible colours. If we take one color of eeach sock, then take one more we will have at leasr 1 pair of 1 color: 3+1=4
(b) We must repeat process in (a) twice: 4+4=8
(c) If the first 16 we take all happen to be black and the next may 10 happen to be red so we have two matching pairs: 26 socks needed
(d) I think once all the blacks and reds are gone, we only need to take 2 more which will inevitibly be blue: 10+16+2=28.
I have a test so I appreciate it if anyone could please correct me.