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# Probability car accidents

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Director
Joined: 23 Apr 2010
Posts: 593
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Kudos [?]: 14 [0], given: 7

Probability car accidents [#permalink]  07 Jun 2010, 03:34
00:00

Question Stats:

50% (01:45) correct 50% (01:33) wrong based on 2 sessions
If 7 distinct car accidents happened during 7 days, what is the probability that all the accidents happened on a particular day?

Official solution:

[Reveal] Spoiler:
OMEGA = 7^7
A = 7
P(A) A/OMEGA = 1/(7^6)

I don't understand the formula for counting the sample space. Your inputs/explanation would be very appreciated.

Thanks.
Manager
Joined: 04 May 2010
Posts: 89
WE 1: 2 yrs - Oilfield Service
Followers: 8

Kudos [?]: 45 [0], given: 7

Re: Probability car accidents [#permalink]  07 Jun 2010, 04:09
In general, the number of ways that "m" objects can be distributed into "n" boxes is n^m (When the objects and boxes are distinguishable, and a box can be empty) I've attached a little reference chart for you to remember the formula for these kind of problems. For the GMAT I wouldn't bother deriving them - just remember them.

So distributing the 7 boxes into the 7 days needs 7^7 ways.

It must be clear to you that if all 7 happened on the same day, it could happen in 7 ways, (since it depends on which day this happened)

Prob = 7 / 7^7 = 1 / 7^6
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File comment: Here's a nice little chart for these kind of repetition problems.

Combinatorics.jpg [ 18.18 KiB | Viewed 970 times ]

Director
Joined: 23 Apr 2010
Posts: 593
Followers: 2

Kudos [?]: 14 [0], given: 7

Re: Probability car accidents [#permalink]  07 Jun 2010, 06:05
Re: Probability car accidents   [#permalink] 07 Jun 2010, 06:05
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