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# A hat contains 18 raffle tickets, numbered 1 through 18. If

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Joined: 07 Jun 2014
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A hat contains 18 raffle tickets, numbered 1 through 18. If [#permalink]  24 Nov 2017, 20:43
Expert's post
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Question Stats:

92% (01:09) correct 7% (00:32) wrong based on 14 sessions
A hat contains 18 raffle tickets, numbered 1 through 18. If two raffle tickets are chosen at random from the hat, what is the probability that both tickets are even numbers?

A. $$\frac{2}{9}$$
B. $$\frac{4}{17}$$
C. $$\frac{1}{4}$$
D. $$\frac{1}{2}$$
E. $$\frac{33}{34}$$

Drill 1
Question: 8
Page: 522
[Reveal] Spoiler: OA

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Sandy
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Joined: 20 Apr 2016
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Kudos [?]: 709 [1] , given: 152

Re: A hat contains 18 raffle tickets, numbered 1 through 18. If [#permalink]  02 Dec 2017, 10:41
1
KUDOS
sandy wrote:
A hat contains 18 raffle tickets, numbered 1 through 18. If two raffle tickets are chosen at random from the hat, what is the probability that both tickets are even numbers?

A. $$\frac{2}{9}$$
B. $$\frac{4}{17}$$
C. $$\frac{1}{4}$$
D. $$\frac{1}{2}$$
E. $$\frac{33}{34}$$

Drill 1
Question: 8
Page: 522

Here
In the number from 1 to 18,
number of even numbers = 9

number of odd numbers = 9

Therefore probability of picking two even numbers = $$\frac{9}{18} * \frac{8}{17}$$ = $$\frac{4}{17}$$
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 123

Kudos [?]: 1975 [0], given: 397

Re: A hat contains 18 raffle tickets, numbered 1 through 18. If [#permalink]  10 Dec 2017, 13:17
Expert's post
Explanation

Think of this problem as if you’re pulling out an even ticket and then another even ticket.

So, for the first ticket there are 9 possible evens out of 18 total, so the probability that the first ticket is even is $$\frac{9}{18}$$. Now you have one fewer even ticket in the hat. So there are 8 evens out of 17 total tickets for the second ticket, thus, the probability is $$\frac{8}{17}$$. You want an even AND aneven, so multiply: $$\frac{9}{18}\times\frac{8}{17}=\frac{4}{17}$$.

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Sandy
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Joined: 02 Aug 2017
Posts: 24
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Re: A hat contains 18 raffle tickets, numbered 1 through 18. If [#permalink]  17 Mar 2018, 23:50
there are 9 even numbers between 1 to 18(inclusive).
total outcomes=18C2
total favourable outcomes=9C2
probability=9C2/18C2 =4/17
Re: A hat contains 18 raffle tickets, numbered 1 through 18. If   [#permalink] 17 Mar 2018, 23:50
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