Question

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 ​$12. ​(B)  The probability of winning all bills in the urn. ​(C)  The probability of the game stopping at the second draw.

Answer 1

Sol Given That, An uon contains 2 one-dollar bills, I five-dollar bill and I ten dollar bill. A player player draws bills one at a time with out replacement from the until ten- dollar bill is drawn. Then The game stops. Total number of bills = 2+1+1 = 4 A) Probability of winning $12 The possibilities are - ( $1, $1, $10) So, P(winning $12) - (W) (5) (+) 12 B) Probability of winning all bills The possibilities ave: ( $,$,$s, $10) ( $', $s, $, $10) ($5, $1, $1, $10)

i. The required probability is (****) + ( ***)+(+****) 2 10 0.25 4 Alternaté melhod probability Required P (not $10 first draw) P (not $10 second draw) * P (not $10 third drow) #P($10 on fourth draw) (-)*(-$) * (1-4)* * 3 45 {x! 0.25 c) The probability of game stopping at the second draw P (any bill except $10 on first draw) * P( $10 10 on second draw) () *(5) - 0.25