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07 Jun 2010, 03:34
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57% (00:44) correct
43%
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If 7 distinct car accidents happened during 7 days, what is the probability that all the accidents happened on a particular day?
Official solution:
I don't understand the formula for counting the sample space. Your inputs/explanation would be very appreciated.
Thanks.
Official solution:
OMEGA = 7^7
A = 7
P(A) A/OMEGA = 1/(7^6)
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.
07 Jun 2010, 04:09
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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
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
Attachments
File comment: Here's a nice little chart for these kind of repetition problems.
Combinatorics.jpg [ 18.18 KiB | Viewed 9970 times ]
