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# A has 3 shares in a lottery containing 3 prizes and 9

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Manager
Joined: 24 Jan 2004
Posts: 55
A has 3 shares in a lottery containing 3 prizes and 9  [#permalink]

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01 Jun 2004, 19:35
A has 3 shares in a lottery containing 3 prizes and 9 blanks; B has 2 shares in a lottery containg 2 prizes and 6 blanks; Compare their chances of success.
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Mayur
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Joined: 30 Oct 2003
Posts: 1187
Location: NewJersey USA
Re: A has 3 shares in a lottery containing 3 prizes and 9  [#permalink]

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02 Jun 2004, 07:03
W - Winning ticket L - loosing ticket

WLL, WWL, WWW
WLL = 3C1 * 9C2
WWL = 3C2 * 9C1
WWW = 3C3 * 9C0

No of ways to chose 3 tickes out of 12 = 12C3

P(A) = ( 3C1 * 9C2 + 3C2 * 9C1 + 3C3 * 9C0 ) / 12C3 = 34/55

P(B) = ( 2C2 * 6C0 + 2C1 * 6C1 ) / 8C2 = 12/28
Manager
Joined: 24 Jan 2004
Posts: 55
Re: A has 3 shares in a lottery containing 3 prizes and 9  [#permalink]

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02 Jun 2004, 08:35
You have done it, but: -

P(B) = ( 2C2 * 6C0 + 2C1 * 6C1 ) / 8C2 = 13/28

so P(A):P(b) = 34/55:13/28 = 952:715
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Mayur
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Joined: 02 Jun 2004
Posts: 119
Location: san jose,ca
A has 3 shares in a lottery containing 3 prizes and 9  [#permalink]

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03 Jun 2004, 00:51
Easier way would be to compute chances for loosing.

P(A loosing)= 9C3/12C3=21/55 so,P(A winning)=34/55
P(B loosing)=6C2/8C2=15/28 so,P(B)=13/28
A has 3 shares in a lottery containing 3 prizes and 9   [#permalink] 03 Jun 2004, 00:51