A man is known to speak truth 1 out of 5 times . He throws a dice and

Question

A man is known to speak truth 1 out of 5 times . He throws a dice and report that it is a six. What is the probability that it is actually a six?

a)  7/10

b)  7/30

c) 1/30

d) 1/21

e) 1/23

yashikaaggarwal · Answer

The probability of him Speaking truth*probability of 6 in dice
1/5*1/6 = 1/30

Answer is C

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ToddB · Answer

5 times 6 equals 30
so the answer is 1/30

ramlala · Answer

Probability to speak truth =  1/5 
Probability to get six =  1/6

Probability of actually get six =  1/6 * 1/5  =  1/30

CrackverbalGMAT · Answer

Solution:

Probability that the man speaks the truth = 1/5

Probability of a six =1/6

Probability the man reports it is a 6 given that a number IS A 6 = 1/5 * 1/6 = 1/30  (option c)

Alternately, you can use Bayes' theorem(though it is usually not tested in a GMAT paper)

Devmitra Sen(GMAT SME)

Bunuel · Answer

The wording of the question is not good but the answer is not 1/30. One can interpret the question in the following two ways:

1. If the die shows anything but a "six" and the man lies, he ALWAYS says it is a "six":

Probability = (The number of favorable outcomes)/(The total number of possible outcomes).

Favorable outcome is that it's actually a "six" and he's telling the truth  =\frac{1}{6}*\frac{1}{5}=\frac{1}{30}

Possible outcomes is: either it's a "six" and he's telling the truth OR it's not a "six" and he's telling the lie  =\frac{1}{6}*\frac{1}{5}+\frac{5}{6}*\frac{4}{5}=\frac{7}{10}

P=\frac{\frac{1}{30}}{\frac{7}{10}}=\frac{1}{21} .

Answer: D.

2. If die shows x and the man lies, he reports any of the other 5 numbers with equal probability of 1/5 for each  For example, say the man rolled a "one" and he lies, then he can say it's a "two", "three", "four", "five" or "six" - each having a probability of 1/5.  I think this reading is more accurate then the first one.  But this reading also assumes that the man tells believable/adequate lie, meaning that he does not say that he rolled a "purple" or a "134" or something like that.

Probability = (The number of favorable outcomes)/(The total number of possible outcomes).

Favorable outcome is that it's actually a "six" and he's telling the truth  =\frac{1}{6}*\frac{1}{5}=\frac{1}{30}

Possible outcomes is: either it's a "six" and he's telling the truth OR it's not a "six" and he's telling a lie and the lie is that it's a "six" =\frac{1}{6}*\frac{1}{5}+\frac{5}{6}*\frac{4}{5}*\frac{1}{5}=\frac{1}{6}

P=\frac{\frac{1}{30}}{\frac{1}{6}}=\frac{1}{5} .

Answer is not among options.

4B51R4 · Answer

Answer should be D. 1/21

Two known facts given in the question are:
Probability of him speaking the truth is 1/5.
He reports the dice to be six.

Given that we know he is only reporting the dice as six, we don't actually know if he's telling the truth or not.
So, what we should be calculating is - (probability he tells the truth and it is actually six) / { (probability he tells the truth and it is actually six) + (probability he is lying and it is not six) }

probability he tells the truth and it is actually six - 1/6 * 1/5 = 1/30

probability he is lying and it is not six - 5/6 * 4/5 = 20/30

Therefore answer should be - (1/30) / { (1/30) + (20/30) } = (1/30) / (21/30) = 1/21

yashikaaggarwal · Answer

But doesn't rest 29/30 displays the man's lying tendency? Why did we got 7/10?

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4B51R4 · Answer

There are 4 outcomes.
The dice is 6 | the man speaks truth and reports it as 6. Probability- 1/6 * 1/5 = 1/30
The dice is not 6 | the man lies and reports it as 6. Probability- 5/6 * 4/5 = 20/30
The dice is not 6 | the man tells the truth and reports the correct no. Probability- 5/6*1/5= 5/30
The dice is 6 | the man lies and reports it as some other no. Probability- 1/6 * 4/5 = 4/30

Since the question states that the man reports the dice to be 6, we can remove outcome 3 and 4 from consideration. I'm not sure weather GMAT tests conditional probability, but it was heavily tested on JEE. I recommend you watch some videos on the topic.

globaldesi · Answer

Agree  Bunuel  . although the official answer is C, I calculated more scenarios which are not covered here. Posted this question specifically to know where was I going wrong. The source was some local book for GMAT.

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A man is known to speak truth 1 out of 5 times . He throws a dice and

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