probability+consecutive integer confusion

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Gurpinder: Legendary Member; Posts: 659; Joined: Mon Dec 14, 2009 8:12 amFollowed by: 3 members; Thanked: 32 times

by Gurpinder » Fri Aug 06, 2010 11:27 am

Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?

OA: [spoiler]2/5[/spoiler]

I know how to get the answer to this problem. BUT I don't understand one thing.

350-101=249. How are there 250 integers from 101 to 350....when I get 249.

Thanks,

"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.

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Source: Beat The GMAT — Problem Solving | Fri Aug 06, 2010 11:27 am

selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Fri Aug 06, 2010 11:34 am

Total tickets=250

Tickets that have a number with 100's digit 2=100[200 to 299]

Prob=Favorable outcomes/Total outcomes=100/250=2/5

It's 101 to 350 inclusive(ie)350-101+1=250

350-101=249 means 249 numbers after 101.But ur not including 101.

Hope this clarify..

--Anand--

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Apr 13, 2015 5:24 am

Gurpinder wrote:Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?

OA: [spoiler]2/5[/spoiler]

I know how to get the answer to this problem. BUT I don't understand one thing.

350-101=249. How are there 250 integers from 101 to 350....when I get 249.

Thanks,

Solution:

The probability of an event is equal to: favorable outcomes/total outcomes

In this particular problem we have:

favorable outcomes = numbers with a hundreds digit of 2

total outcomes = consecutive integers from 101 through 350

Let's start with the total outcomes. Although the word "inclusive" is not actually used, it is implied because we are told the raffle tickets start at 101 and end at 350. Thus, the number of tickets from 101 to 350, inclusive, is 350 - 101 + 1 = 250. (Note that we had to add 1 because we counted BOTH tickets 101 and 350.)

The favorable outcomes are the number of tickets with a hundreds digit of 2. Since all the numbers from 200 to 299 are included, there are 299 - 200 +1 = 100 numbers with a hundreds digit of 2.

Therefore, the probability that a randomly selected ticket with have a hundreds digit of 2 is 100/250 = 2/5.

The answer is A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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