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# A speaks the truth 3 times out of 4, B speaks the truth 7 times out of

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A speaks the truth 3 times out of 4, B speaks the truth 7 times out of  [#permalink]

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23 Jan 2020, 01:17
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Difficulty:

25% (medium)

Question Stats:

87% (01:25) correct 13% (01:30) wrong based on 15 sessions

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A speaks the truth 3 times out of 4, B speaks the truth 7 times out of 10. They both assert that a white ball is drawn from a bag containing 6 balls, all of different colors. What is the probability of the truth of the assertion.

A. $$\frac{12}{49}$$

B. $$\frac{3}{10}$$

C. $$\frac{21}{40}$$

D. $$\frac{3}{40}$$

E. None of these

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Re: A speaks the truth 3 times out of 4, B speaks the truth 7 times out of  [#permalink]

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23 Jan 2020, 04:15
Bunuel wrote:
A speaks the truth 3 times out of 4, B speaks the truth 7 times out of 10. They both assert that a white ball is drawn from a bag containing 6 balls, all of different colors. What is the probability of the truth of the assertion.

A. $$\frac{12}{49}$$

B. $$\frac{3}{10}$$

C. $$\frac{21}{40}$$

D. $$\frac{3}{40}$$

E. None of these

Truth speaking rate of A = 3/4
Truth speaking rate of A = 7/10

Probability of truth assertion = (3/4)*(7/10) = 21/40

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A speaks the truth 3 times out of 4, B speaks the truth 7 times out of  [#permalink]

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23 Jan 2020, 08:02
GMATinsight wrote:
Bunuel wrote:
A speaks the truth 3 times out of 4, B speaks the truth 7 times out of 10. They both assert that a white ball is drawn from a bag containing 6 balls, all of different colors. What is the probability of the truth of the assertion.

A. $$\frac{12}{49}$$

B. $$\frac{3}{10}$$

C. $$\frac{21}{40}$$

D. $$\frac{3}{40}$$

E. None of these

Truth speaking rate of A = 3/4
Truth speaking rate of A = 7/10

Probability of truth assertion = (3/4)*(7/10) = 21/40

Hey GMATinsight

Why do we not consider the probability of drawing a white ball (1/6) here?

Posted from my mobile device
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Re: A speaks the truth 3 times out of 4, B speaks the truth 7 times out of  [#permalink]

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24 Jan 2020, 00:23
firas92 wrote:
GMATinsight wrote:
Bunuel wrote:
A speaks the truth 3 times out of 4, B speaks the truth 7 times out of 10. They both assert that a white ball is drawn from a bag containing 6 balls, all of different colors. What is the probability of the truth of the assertion.

A. $$\frac{12}{49}$$

B. $$\frac{3}{10}$$

C. $$\frac{21}{40}$$

D. $$\frac{3}{40}$$

E. None of these

Truth speaking rate of A = 3/4
Truth speaking rate of A = 7/10

Probability of truth assertion = (3/4)*(7/10) = 21/40

Hey GMATinsight

Why do we not consider the probability of drawing a white ball (1/6) here?

Posted from my mobile device

The qquestion is not about it being white ball. Question is about two of them speaking truth simultanuously... hence th eprobability includes on the probability of them speaking truth together,
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Re: A speaks the truth 3 times out of 4, B speaks the truth 7 times out of  [#permalink]

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27 Jan 2020, 08:56
1
The answer is clearly not 21/40. That's easy to see by just changing the question setup:

"A tells the truth 3/4 of the time, and B tells the truth 7/10 of the time. A bag contains one white marble, and a marble is picked from the bag. Both A and B assert that the marble is white. What is the probability they are telling the truth?"

Obviously the answer is 1, not 21/40. The prior likelihood of picking the white marble matters. It also matters what they say when they are not telling the truth. If A always says "that's not a marble, it's an avocado" when he lies, then when he says the marble selected is white, it must be true. If he tells plausible lies, then it becomes less certain. Nor do we even know there's a white marble in the bag (the question doesn't say there is), so it's possible the probability their assertion is true is zero.

The wording of the question is far too unclear for the question to be answerable, and it's not properly thought out if the answer is meant to be C.
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Re: A speaks the truth 3 times out of 4, B speaks the truth 7 times out of  [#permalink]

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28 Jan 2020, 03:03
Bunuel

Re: A speaks the truth 3 times out of 4, B speaks the truth 7 times out of   [#permalink] 28 Jan 2020, 03:03
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