An urn contains 2 one-dollar bills, 1 five-dollar bill and 1 ten-dollar bill. A player draws bills one at a time without replacement from the urn until a ten-dollar bill is drawn. Then the game stops. All bills are kept by the player. Determine: (A) The probability of winning $15. (B) The probability of winning all bills in the urn. (C) The probability of the game stopping at the second draw.

Given that an urn contains 2 one-dollar bills, 1 five-dollar bill and 1 ten-dollar bill. A player draws bills one at a time without replacement from the urn until a ten-dollar bill is drawn.

The 10 dollar bill can be drawn either in I draw or II draw or III draw.

A) Prob of drawing 15 = Prob of drawing 5 in I draw and 10 in II draw

[tex]\frac{1}{4} *\frac{1}{3} =\frac{1}{12}[/tex]

B) The probability of winning all bills in the urn.=Prob of drawing 10 dollar bill in IV draw = Prob of drawing one or 5 dollar in first three draws and last draw 10 dollar

= [tex]\frac{2}{4} *\frac{1}{3} *\frac{1}{2} +\frac{1}{4}* \frac{2}{3}* \frac{1}{2 } \\\\=\frac{1}{6}[/tex]

C) Prob of game stopping at second drawn = Prob of I draw non 10 and second draw 10

= [tex]\frac{3}{4}* \frac{1}{3} \\=\frac{1}{4}[/tex]