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# Two canoe riders must be selected from each of two groups of

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Director
Joined: 07 Nov 2004
Posts: 694
Followers: 4

Kudos [?]: 29 [0], given: 0

Two canoe riders must be selected from each of two groups of [#permalink]  02 Jan 2005, 08:19
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Question Stats:

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Two canoe riders must be selected from each of two groups of campers. One group consists of three men and one woman, and the other group consists of two women and one man. What is the probability that two men and two women will be selected?

(A) 1/6
(B) 1/4
(C) 2/7
(D) 1/3
(E) 1/2
Current Student
Joined: 28 Dec 2004
Posts: 3391
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 181 [0], given: 2

Re: PS: Canoe Riders [#permalink]  02 Jan 2005, 10:25
I am very weak in Prob and really dont even practice for em.... but my answer is 1/3 (D)

we have 2 groups Group1 and Group2 and we have 2 slots each to fill

Group1 we can M1W1 W1M1 M1M1 (prob find a man is 2/3 on first try 1/2 on next) (prob find a W first is 1/3 and 1 for finding M on next slot)

Same thing for Group2

so we can have following combinations from group1 (M1W1 W1M1 M1M1)
we can have the following combinations from group2 (W2M2 M2W2 W2W2)

adding all the possibilities, i get 3/9 = 1/3!
I am pretty certain i could be wrong, but on exam day I just hope I get to only see 1 or 2 prob question.

gayathri wrote:
Two canoe riders must be selected from each of two groups of campers. One group consists of three men and one woman, and the other group consists of two women and one man. What is the probability that two men and two women will be selected?

(A) 1/6
(B) 1/4
(C) 2/7
(D) 1/3
(E) 1/2
VP
Joined: 18 Nov 2004
Posts: 1442
Followers: 2

Kudos [?]: 20 [0], given: 0

"E".

Total ways to select 4 ppl : 4C2*3C2 = 18

Number of likely ways : Scenario 1: 2M selected from Gp1 and 2 W selected from gp 2 = 3C2*1 = 3

Scenario 2: 1M and 1W selected from gp 1 and 1M and 1 W from gp 2
= 3C1*1*2C1*1 = 6

P(e) = 6+3 / 18 = 1/2
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