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# In a certain game, what is the probability that Martha wins the first

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Manager
Joined: 27 Jan 2016
Posts: 150
Schools: ISB '18
GMAT 1: 700 Q50 V34
In a certain game, what is the probability that Martha wins the first [#permalink]

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04 Aug 2017, 11:22
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75% (hard)

Question Stats:

29% (00:55) correct 71% (01:03) wrong based on 68 sessions

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In a certain game, what is the probability that Martha wins the first 5 rounds and loses the sixth?

(1) The chance that Martha wins the first 4 rounds and loses the fifth is $$\frac{1}{32}$$.

(2) The chance that Martha wins the first 6 rounds and loses the seventh is $$\frac{1}{128}$$.
[Reveal] Spoiler: OA
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4680
Re: In a certain game, what is the probability that Martha wins the first [#permalink]

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04 Aug 2017, 13:24
srikanth9502 wrote:
In a certain game, what is the probability that Martha wins the first 5 rounds and loses the sixth?
Statement #1: The chance that Martha wins the first 4 rounds and loses the fifth is .
Statement #2: The chance that Martha wins the first 6 rounds and loses the seventh is .

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are not sufficient

Dear srikanth9502,

My friend, apparently you copy & pasted this question from some other source, and the math expressions, presumably the fraction given for the probabilities, did not copy, so both statement end with an awkward blank, rather than mathematical information. Please fill in those fractions.

Mike
_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4680
Re: In a certain game, what is the probability that Martha wins the first [#permalink]

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04 Aug 2017, 13:37
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Expert's post
srikanth9502 wrote:
In a certain game, what is the probability that Martha wins the first 5 rounds and loses the sixth?
Statement #1: The chance that Martha wins the first 4 rounds and loses the fifth is $$\tfrac{1}{32}$$.
Statement #2: The chance that Martha wins the first 6 rounds and loses the seventh is $$\tfrac{1}{128}$$.

Dear srikanth9502,

OK, I found the correct fractions on another website. My friend, please be careful in posting anything here: please double-check that all parts of a problem have been correctly copied. In preparing for the GMAT, every detail matters. My friend, how you do anything is how you do everything.

What this question is trying to do is lull us into a pattern, thinking that it should be reciprocals of the powers of 2. If the game is something that gets twice as hard to win each time, then of course, the missing probability, the probability of winning the first 5 and losing the 6th, would be 1/64. That is the tempting mistake to make.

In fact, we know nothing about the nature of the game and how its rounds work. Perhaps the rule is that winning the 5th round automatically means that one wins the 6th round, so this probability would be zero. Perhaps, there's some other rule, and the probability is 10% or 85% or something else. We really have no idea at all.

OA = (E)

This question pulls a cheap trick and tries to fool students. This is not really a well thought out question. Here's a much better DS question:
Value of Square of Binomial

Does all this make sense?
Mike
_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Re: In a certain game, what is the probability that Martha wins the first   [#permalink] 04 Aug 2017, 13:37
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