4 0
S _ C K S .
I F
H _
T _ K _ S
_ _ T
3 8
S _ C K S ,
_ L T H _ _ G H
_ T
_ S
V _ R Y
_ N L _ K _ L Y ,
_ T
_ S
P _ S S _ B L _
T H _ Y
C _ _ L D
_ L L
B _
B L _ _
_ N D
R _ D .
T _
B _
1 0 0
P _ R C _ N T
C _ R T _ _ N
T H _ T
H _
_ L S _
H _ S
_
P _ _ R
_ F
B L _ C K
S _ C K S
H _
M _ S T
T _ K _
_ _ T
_
F _ R T H _ R
T W _
M _ R _
S _ C K S Clue
THE PROBABILITY OF TAKING OUT A PAIR OF BLACK SOCKS IS ZERO. IF THERE'S A WHITE PAIR AND BLACK PAIR OF SOCKS, THERE WOULD HAVE BEEN THREE CASES: BLACK PAIR, WHITE PAIR, MIXED PAIR. THIS WOULD GIVE A PROBABILITY OF 1/3 FOR A PAIR OF WHITE SOCKS. BUT THEN, IT IS STATED THAT THE PROBABILITY OF WHITE SOCKS IS 1/2 OR ONLY 2 POSSIBILITIES. THIS MEANS THERE THAT THERE WAS NO BLACK PAIR. WE CAN CONCLUDE THAT THERE WERE THREE WHITE SOCKS AND ONE BLACK SOCK YOU NEED TO TAKE OUT THREE SOCKS. TO HAVE A MATCHING PAIR, YOU NEED TO TAKE 2 SOCKS THAT ARE OF THE SAME COLOR. WHEN YOU TAKE 3 SOCKS, 2 OF THE SOCKS WILL BE OF THE SAME COLOR FIVE. THERE ARE ONLY FOUR COLORS, SO FIVE SOCKS WILL GUARANTEE THAT TWO WILL BE THE SAME COLOR 40 SOCKS. IF HE TAKES OUT 38 SOCKS, ALTHOUGH IT IS VERY UNLIKELY, IT IS POSSIBLE THEY COULD ALL BE BLUE AND RED. TO BE 100 PERCENT CERTAIN THAT HE ALSO HAS A PAIR OF BLACK SOCKS HE MUST TAKE OUT A FURTHER TWO MORE SOCKS