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
(This question was demanded by Ferozy and Niharika )
Demand a GRE Question: Probability
Subscribe / Share
I THINK ANS IS ——–A
PERSON SPEAKS 75% OF TRUTH THAT IS GIVEN 3/4
HE THROWS THE DICE ONCE AND CHANCES OF TELLING THE TRUTH THAT IT IS 6 IS ALSO 3/4
BUT IF HE THROWS TWO TIMES THEN THE CHANCES OF TELLING TRUTH IS 3/4*3/4=9/16
IS MY APPROACH AND UNDERSTANDING CORRECT
THANKS
ferozy rocks!
me tooo 3/4
any one else like to attempt ?
welll guys n mr gre admin…i think the answer is 3/8 which is nt the given options……..
it goes like this…..
using the concept of mutually exclusive events… the probability of the number actually being 6 is…..considering he lies once in 4 times…(1/4)…
let…
a=3/4(prob. oh him saying truth..)
á=1/4(prob of him lieing…)
b=1/6(prob of falling 6..)
b^=5/6(prob of not falling of 6..)
then…
(its actually a theorem nt sure wht it is…hmm i don suppose gre asks ques of this standard tho..newayss..)
P=a*b/(a*b+á*b^)
=>
P=3/8…..
answer is 8/24 which is 1/3….not given choice jsut take prob. telling truth + prob telling lie since this is a mutually exclusive event….
the case could be six should come and he should say the truth
so (1/6)*(3/4)
not an option???????
plz hepl team
I agree with Devesh, it should be (1/6)*(3/4)
Prob. of his telling the truth = 3/4
Prob. of 6 actually coming = 1/6
So, the prob. that the no. actualy is a 6 = (1/6)*(3/4)
Sorry,
a few modifications, it shud be like this :-
(1/6)*(3/4) + (1/6)*(1/4) = 4/24 = 1/6
(1/6)*(3/4) = Prob of his getting a 6 and speaking the truth
(1/6)*(1/4) = Prob. of his getting a six and telling a lie.
Admin please help . . .
i go with what devesh had said.. 1/6 * 3/4 = 1/8
bcoz the ques asks for the prob that it is actually a 6.. which i think translates into the prob of getting a 6 and the prob that he speaks the truth.
3/4 is the answer
very simple question since he reports success even as 6 and
we know that he always speak 3/4 time truth
so taking this ratio on
3*2=6
so as 4 comes to 8
solving it get 3/4
i think this is level 2 question for actual GRE
plz wat’s the ans team?
i think the answer should be
(1/6 * 3/4 ) + ( 5/6* 1/4)
= 8/24
Answer is
a) 3/4
prob of speaking truth is the answer
3/4
it’s just 3/4 since all that needs to be checked is the probabilty of him telling the truth..if he says its a six then the prob of that happening is 3/4 n otherwise 1/4..the chance of a 6 falling can be ignored… so the answer is [a]
8/24 would be the probability of the person “sayin that it is a 6″ rather than it being a six when he claims so
Correct answer is A
LOOK, there is a slight ambiguity to the queston. u cld look at it two ways.
1) we are concerned with th number 6 being on the dice…. in which case, its 1/6(prob of gettin a 6) * 3/4 (prob of his speakin the truth)…………. in which case the ans is 1/8………… but this option is not there
2) the actual hidden question is only whether or not he is speakin the truth. ie, is there a match betwn wat this guy says n wats really seen on the dice. ? then it would simply be 3/4………. that option is available so we go with (A)…………
Great q admin. thanks ferozy…….. such booby traps always show up on the gre
i think its 3/4.we need to consider whether he is speaking the truth or not ,thats it!
I am not convinced with the answer A. (the way ferozy has thought is brilliant though!) But while calculating risks (ie, situations similar to these) we cannot say it is depends on the person. Well, here is my reasoning:
How did you come to the decision that he lies 3 times?? It is by a statics. Hence a logical continuation of it would be to choose a probabilistic approach.
So, 3/4 * 1/6= 1/8 is most ‘probable’ !!!!
I also think that answer choices are wrong. The answer should be 3/8. This requires use of conditional probabilities and bayes theoram.
Let A be the Event that a 6 was thrown and B be the event that He says 6 was thrown. We want to find P (A|B)
We know that P(A|B)P(B) = P(B|A)P(A)
=> P (A|B) = (P(B|A) * P(A)) /P(B)
P(B|A) = 3/4
P(A) = 1/6
P(B) = 1/6 * 3/4 + 5/6 * 1/4 = 3/24 + 5/24 = 8/24 = 1/3
=> P(A|B) = (3/4) * (1/6) / (1/3) = 3/8
HEY JERRY PL EXPLAIN THIS IN DETAIL.IT WOULD BE OF GREAT HELP IF YOU DO SO SINCE I FIND SOMETHING SUBTLE IN UR ASSERTION. THNAK YOU — 8/24 would be the probability of the person “sayin that it is a 6″ rather than it being a six when he claims so
i agree with one of the answer & i am getting the same answer
The answer iam getting is 1/6
there are basically two cases to be considered
1)he is telling the truth & the dice throw is 6.
2)he is lying & the dice throw is 6.
so add 1 & 2.
the answer is 4/24 which is 1/6.
well guys, its pretty simple …. the probability that is required is the probability of the die actually having shown a six. So, when this happens (when its actually six) , the man says the truth!!!!(straight forward). Therefore , the probability of this event is the probaility of the man saying the truth which is 3/4.(you dont have to consider the probability of him lying because , its obvious that he says the truth when its actually six)
take simple question in simple way.. dont apply too much complicated thinking. correct answer is A
i need to say again what sanjeev said take simple question in simple way.. dont apply too much complicated thinking. correct answer is A
i dont get any thing
A
THE QUESTION IS NOT CLEAR
I think many people have not taken note of the question properly and many do not know Bayes theorem or what is known as inverse probability this will be one of the last 10 questions if the score is going to be 800 .
The answer should be 3/8. This requires use of conditional probabilities and bayes theoram.
Let A be the Event that a 6 was thrown and B be the event that He says 6 was thrown. We want to find P (A|B)
We know that P(A|B)P(B) = P(B|A)P(A)
=> P (A|B) = (P(B|A) * P(A)) /P(B)
P(B|A) = 3/4
P(A) = 1/6
P(B) = 1/6 * 3/4 + 5/6 * 1/4 = 3/24 + 5/24 = 8/24 = 1/3
=> P(A|B) = (3/4) * (1/6) / (1/3) = 3/8
its a contentious issue! but what the question asks is what is the chance that he reports a correct result of the thrown die, therefore theyr just asking whether hes telling the truth or not. Mathematically, the answer is 3/4 coz if he is telling the truth then its a six and u need not multiply by 1/6 so the answers just 3/4.
cheerio.
well daer the answer is (a) as the probbility of the guy to speak truth is 3/4
and that’s what in this statement the truth depends 3/4 times
i agree wit K2..it makes sense…
The answer is 3/8
Explanation :- There are two cases
True 3/4 & lie 1/4
Let he speek trueth that it is 6 then we have chance = 3/4 x 1/6 = 3/24
or he tell a lie that it is 6 = 1/4 x 5/6 = 5/24
So, required probability is = 3/24 /( 3/24 + 5/24)
= 3/8
can anyone give me good gre-toefl preparation sites
and if anyone has collection of gre/toelf recent question please help me by mailing to pattar_raj@yahoo.com thxs 1-n-all
well i dont think this question requires so much discussion as it is aksed what is prob of truth cant u see that its gvn is question man work smartly not like a ass
its offcourse 3/4
a