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# There is a group of six people; among them are Mr X and Mr

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SVP
Joined: 03 Feb 2003
Posts: 1608
Followers: 6

Kudos [?]: 76 [0], given: 0

There is a group of six people; among them are Mr X and Mr [#permalink]  11 Jun 2004, 23:52
There is a group of six people; among them are Mr X and Mr Y. Three persons are chosen at random without repetitions. Find the probability of choosing:

1) Mr X, but not Mr Y.
2) Both Mr X and Mr Y.
3) Neither Mr X nor Mr Y.
4) Either Mr X or Mr Y, but not both.
5) Either Mr X or Mr Y or both.
Manager
Joined: 07 May 2004
Posts: 183
Location: Ukraine, Russia(part-time)
Followers: 2

Kudos [?]: 8 [0], given: 0

Re: some complex probability problem [#permalink]  12 Jun 2004, 00:40
stolyar wrote:
There is a group of six people; among them are Mr X and Mr Y. Three persons are chosen at random without repetitions. Find the probability of choosing:

1) Mr X, but not Mr Y.
2) Both Mr X and Mr Y.
3) Neither Mr X nor Mr Y.
4) Either Mr X or Mr Y, but not both.
5) Either Mr X or Mr Y or both.

1. C[2,4]/C[3,6] = 36/120 = 6/20 = 3/10.

2. C[1,4]/C[3,6] = 4*6*6/(6*120) = 1/5.

3. C[3,4]/C[3,6] = 1/5.

4. 2*P(X, but not Y) = 6/10 = 3/5.

5. P(X or Y, but not both) + P(both) = 3/5 + 1/5 = 4/5.
SVP
Joined: 03 Feb 2003
Posts: 1608
Followers: 6

Kudos [?]: 76 [0], given: 0

Agree

(1) 0.3
(2) 0.2
(3) 0.2
(4) 0.6
(5) 0.8
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