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A bowl contains 18 raffle tickets, numbered 1 through 18.

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A bowl contains 18 raffle tickets, numbered 1 through 18. [#permalink]

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New post 01 Oct 2017, 12:48
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A bowl contains 18 raffle tickets, numbered 1 through 18. If two raffle tickets are chosen at random from the bowl, 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. \(\frac{33}{34}\)
[Reveal] Spoiler: OA

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Re: A bowl contains 18 raffle tickets, numbered 1 through 18. [#permalink]

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Gnpth wrote:
A bowl contains 18 raffle tickets, numbered 1 through 18. If two raffle tickets are chosen at random from the bowl, 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. \(\frac{33}{34}\)



Hi...

There are 9 even numbers out of 18 consecutive integers..
So Q boils down to selecting 2 out of 9... 9P2=\(9!/7!=8*9\)
And total ways are 18*17..
So prob= \(\frac{8*9}{17*18}=4/17\)
B

Also if you work directly on probability..
Prob of picking an even number in first go= 9/18=1/2
Prob of picking an even number then on second go also =1/2 * 8/17=4/17
B
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Re: A bowl contains 18 raffle tickets, numbered 1 through 18. [#permalink]

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New post 02 Oct 2017, 09:07
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Gnpth wrote:
A bowl contains 18 raffle tickets, numbered 1 through 18. If two raffle tickets are chosen at random from the bowl, 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. \(\frac{33}{34}\)


Even numbers are 9 then probability 1st even raffle is 9/18 and for second is 8/17
=9/18*8/17=4/17.. Ans B

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Re: A bowl contains 18 raffle tickets, numbered 1 through 18. [#permalink]

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New post 04 Oct 2017, 16:40
Gnpth wrote:
A bowl contains 18 raffle tickets, numbered 1 through 18. If two raffle tickets are chosen at random from the bowl, 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. \(\frac{33}{34}\)


There is a 9/18 chance of selecting an even number with the first pick and a 8/17 chance of selecting an even number with the next pick; thus, the probability of selecting 2 even numbers is 9/18 x 8/17 = 1/2 x 8/17 = 8/34 = 4/17.

Answer: B
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Re: A bowl contains 18 raffle tickets, numbered 1 through 18.   [#permalink] 04 Oct 2017, 16:40
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A bowl contains 18 raffle tickets, numbered 1 through 18.

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