Chris has a bag with 4 black socks and 6 red socks (so there are 10 socks in total). Timothy reaches into the bag and grabs two socks without replacement. Find the probability that he will not grab two red socks.
+23246 With 4 black socks and 6 red socks, he can end without two red socks in these ways:
1) grabbing two black socks: (4/10)·(3/9) = 12/90
2) grabbing a red sock and then a black sock: (6/10)·(4/9) = 24/90
3) grabbing a black sock and then a red sock: (4/10)·(6/9) = 24/90
Since these are independent: 12/90 + 24/90 + 24/90 = 60/90 = 1/3
The probability that he will not have a pair of red socks: 1/3
