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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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11 Oct 2014, 19:27
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Difficulty:

55% (hard)

Question Stats:

62% (01:43) correct 38% (01:49) wrong based on 109 sessions

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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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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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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.

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

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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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15 Dec 2015, 11:40
Hello from the GMAT Club BumpBot!

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

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18 Dec 2015, 10:47
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Expert's post
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.

[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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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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