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There are two names given JOHNSON and JONES. If one letter is picked

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There are two names given JOHNSON and JONES. If one letter is picked [#permalink]

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There are two names given JOHNSON and JONES. If one letter is picked from both simultaneously at random, then find the probability that the letter is same?

A. 24/35
B. 17/35
C. 8/25
D. 6/35
E. 1/25
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Oct 2014, 02:29, edited 1 time in total.
Renamed the topic.

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Re: There are two names given JOHNSON and JONES. If one letter is picked [#permalink]

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New post 12 Oct 2014, 01:11
eggplantpower wrote:
There are two names given JOHNSON and JONES. If one letter is picked from both simultaneously at random, then find the probability that the letter is same?

A) 24/35
B) 17/35
C) 8/25
D) 6/35
E) 1/25



Can someone explain if the answer D has a typo? i am pretty sure answer is 4/35 but that isnt one of the choices...

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Re: There are two names given JOHNSON and JONES. If one letter is picked [#permalink]

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New post 12 Oct 2014, 02:38
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eggplantpower wrote:
There are two names given JOHNSON and JONES. If one letter is picked from both simultaneously at random, then find the probability that the letter is same?

A. 24/35
B. 17/35
C. 8/25
D. 6/35
E. 1/25


JOHNSON
JONES


The probability that letter J is picked = 1/7*1/5 = 1/35;
The probability that letter O is picked = 2/7*1/5 = 2/35;
The probability that letter N is picked = 2/7*1/5 = 2/35;
The probability that letter S is picked = 1/7*1/5 = 1/35.

The sum of these probabilities = 6/35.

Answer: D.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 3 and 10. Also, please tag questions properly! This is NOT your question!
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Re: There are two names given JOHNSON and JONES. If one letter is picked [#permalink]

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New post 12 Oct 2014, 02:46
JOHNSON - 7 letters
JONES - 5 letters

Common Letters : J, O, N, S

Prob of picking J from both = \(\frac{1}{7}+\frac{1}{5}=\frac{1}{35}\)
Prob of O = \(\frac{2}{7}+\frac{1}{5}=\frac{2}{35}\)
Prob of N = \(\frac{2}{7}+\frac{1}{5}=\frac{2}{35}\)
Prob of S = \(\frac{1}{7}+\frac{1}{5}=\frac{1}{35}\)

Total prob =\(\frac{6}{35}\)

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Re: There are two names given JOHNSON and JONES. If one letter is picked [#permalink]

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New post 15 Dec 2015, 11:40
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Re: There are two names given JOHNSON and JONES. If one letter is picked [#permalink]

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New post 18 Dec 2015, 10:47
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Hi All,

This question can also be solved by using 'brute force' - you just have to 'map out' the possibilities.

The name "Johnson" has 7 letters and the name "Jones" has 5 letters, so there are (7)(5) = 35 possible pairings of letters that can occur.

Of those 35, the pairings that include the SAME letter both times are:

J and J
1st O and O
1st N and N
S and S
2nd O and O
2nd N and N

Total: 6

So the probability that the two randomly selected letters will match is 6/35.

Final Answer:
[Reveal] Spoiler:
D


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Re: There are two names given JOHNSON and JONES. If one letter is picked [#permalink]

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New post 27 Aug 2017, 00:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: There are two names given JOHNSON and JONES. If one letter is picked   [#permalink] 27 Aug 2017, 00:25
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