Three cards are drawn from an ordinary 52-card deck without

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Three cards are drawn from an ordinary 52-card deck without [#permalink]

12 Jan 2005, 06:05

1. Three cards are drawn from an ordinary 52-card deck without
replacement (drawn cards are not placed back in the deck). The probability that none of the three cards is a heart is as follows

(a)39/52
(b)38/51
(c)37/50
(d)703/1700
(e)267/1700

my problem below=>

ok it is a simple problem, but my question concerns the two ways of finding the solution.

1. Prob (first card is not heart ) * Prob (second card is not heart GIVEN THAT first is not heart) * Prob (Third card is not heart GIVEN THAT first two are not hearts) = required Prob

38/52*38/51*37/50=703/1700

2. Prob (first card is heart ) * Prob (second card is heart GIVEN THAT first is heart) * Prob (Third card is heart GIVEN THAT first two are hearts) = Prob => 1-Prob = required Prob

13/52*12/51*11/50=1716/132600=1-1716/132600=1678/1700

can someon explain to me why i get two different solutions ???

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Re: probability 64 [#permalink]

12 Jan 2005, 06:47

It is 39/52 * 38/51 * 37/50 = Ans d:

None of the cards has to be heart. => all the three can be hearts or any one can be heart or any two can be hearts. You need to add up all these before you subtract from 1. That is where the second answer you have given is different.

christoph wrote:

_________________

Awaiting response,

Thnx & Rgds,
Chandra

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[#permalink]

12 Jan 2005, 07:12

right...i misread "none" ! thanx !

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[#permalink]

12 Jan 2005, 10:04

I still get a different answer:

13/52+12/51+11/50=1199/1700
1-1199/1700=501/1700

Why?

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[#permalink]

12 Jan 2005, 10:14

this is a better way to find the solution, cause in your attempt you forgot the possibilty that there are two or one hearts. it is also an AND-problem, so you have to multiply. first draw AND second draw AND third draw.

Prob (first card is not heart ) * Prob (second card is not heart GIVEN THAT first is not heart) * Prob (Third card is not heart GIVEN THAT first two are not hearts) = required Prob

38/52*38/51*37/50=703/1700

[#permalink] 12 Jan 2005, 10:14

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Three cards are drawn from an ordinary 52-card deck without

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Three cards are drawn from an ordinary 52-card deck without

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