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kwame.appau
Prospective Students
 
Posts: 35
Joined: Sat Jan 05, 2013 6:49 am
 

Word Problems

by kwame.appau Thu Feb 27, 2014 1:39 pm

question 3 of the hardest practice question set
please do not understand the explanation give to the solution.

Question: four people each roll a fair die once.
A) the probability that at least two people will roll the same number.
i need the explanation of the above question. thanks
tommywallach
Manhattan Prep Staff
 
Posts: 1917
Joined: Thu Mar 31, 2011 11:18 am
 

Re: Word Problems

by tommywallach Mon Mar 03, 2014 11:24 pm

Hey Kwame,

Anytime a question mentions "at least," it means you're going to use the 1-x trick. This trick is based on the fundamental equation of probability:

P(Event Happening) + P(Event Not Happening) = 1

This is important because we could write the equation like this:

P(At least two people get the same thing) + P(Nobody gets the same thing as anyone else) = 1

Do you see that those two possibilities are ALL the possibilities? And this means we can get the answer by doing this:

P(At least two people get the same thing = 1 - P(Nobody gets the same thing as anyone else)

We do this because it's way easier to solve for P(Nobody gets the same thing as anyone else). To do that we just look at what we need everyone to roll

Person 1: 6/6 (this person can roll anything)
Person 2: 5/6 (this person needs to roll something different from person 1)
Person 3: 4/6 = 2/3 (this person needs to roll something different from both person 1 AND person 2)
Person 4: 3/6 = 1/2 (this person needs to roll something different from peoples 1, 2, and 3).

1 * 5/6 * 2/3 * 1/2 = 10/36 = 5/18

We're almost done. Go back to our original equation:

P(at least two people roll the same thing) = 1 - 5/18 = 13/18

Hope that makes more sense!

-t
kwame.appau
Prospective Students
 
Posts: 35
Joined: Sat Jan 05, 2013 6:49 am
 

Re: Word Problems

by kwame.appau Thu Mar 06, 2014 3:00 pm

Thanks Mr. Wallach this is a very simple explanation
tommywallach
Manhattan Prep Staff
 
Posts: 1917
Joined: Thu Mar 31, 2011 11:18 am
 

Re: Word Problems

by tommywallach Mon Mar 10, 2014 11:25 pm

Glad to help!

-t