A man is known to speak truth 3 out of 4 times. He throws die and reports that it is a 6. The probability that it is actually a 6 is
A) 3/4
B) 5/8
C) 2/5
D) 3/5
E) 4/5
GMAT Question of the Day : Probability
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Hrm.. Seems no one has an answer to this me included
Gmat team, any pointers
I am thinking like this..
probability of getting actual 6 is 1/6
probability of him telling (truth) it as 6 is 3/4
probability of him telling it as 6 and it is actually 6 is ( 1/6*3/4 = 1/8)
– but i don’t see any options
if i consider the probability of not getting 6 i.e 5/6 then I get answer 5/8 — put your thoughts
My answer is 1/6*3/4 = 1/8. But i dont see it in the options and i can’t think of where i went wrong.
Gmat team, some pointers please.
Guys, my guess – A
The question is asking the probability that it is actually 6, which means the probability that he is speaking the truth, which is 3/4
My answer is also A
Given that he reported it is 6, you need to calculate “conditional probability”.
wat krishna said was correct…answer should be 1/8.
i take my words back…it is 3/4 only…sure
If this man rolled the dice and found 5, what would be the probability to say 4? 1/4*1/5=1/20
If the dice in reality was 1 and he said 6. Probability=1/20
If the dice in reality was 2 and he said 6. Probability=1/20
.
.
.
If the dice in reality was 6 and he said 6. Probability=3/4
Answer A
My answer is A.
Instead of a dice if it was a coin. The probability of a heads or tails would be 1/2 no matter who is flipping the coin. So if a liar flips the coin or a person who is not a liar (btw what is the antomyn of a liar?) flips the coin the outcome of a heads or tails is 1/2.
Now lets read last sentence of the question:
“The probability that it is actually a 6 is…”
This sentence asks us “What is the probability that the guy is saying the truth?” The word ACTUALLY is key here.
What can be the answer? 3/4 ofcourse
correct answer is A.
it will be 3/4 ….simple very simple
The question is about man saying truth or not… irrespective of whether dice shows 6 or not..
So i too think that A should be the answer…
its a Question of conditioned probability
probability that he reports a six=prob of its actually 6 + prob he is lying
=1/6 * 3/4 + 5/6 * 1/4
now probability that he speaks truth after he has reported 6=
(1/6 * 3/4 ) / (1/6 * 3/4 + 5/6 * 1/4)
and we get the answer as 3/8
i know my approach is not wrong
please tell me if it is wrong!!!!
Prob tht its a 6 and he speaks truth :- 3/4 * 1/6 = 3/24
Now what is the prob of reporting a 6 on a dice (irresp of whthr it actually is a 6 or not)
if its actually a six and saying truth, then 3/4 *1/6 = 3/24 and
if its not a six and speaking lie tht it is a 6 :- 1/4 (speaking a lie) * 5/6 (prob of no. other than 6) * 1/5 (lieing the number as 6 and not telling any othe number except the actual no.) = 5/120 = 1/24
Thus the prob of reporting no. as 6 is = 3/24 + 1/24 = 4/24 = 1/6
THUS prob of actually having 6 when reported so is = 3/24/1/6 = 3/4
A
thanks dood
i was forgetting the 1/5 factor
A.
its really a tricky ques.
you ask something to the man and probability od his telling truth is 3/4.
so thrwo a die and ask him whether is is 6 or not, and he answers yes its 6.
what is probability that hi told truth….its 3/4.
good.