Just the Facts

Probability Level pending

The probability that John tells the truth is $\frac8{10}$ , and the probability that Paul tells the truth is $\frac57$ . They are both are giving statements to a police officer over a crime that happened. What is the probability that their statements agree?

17\%

34\%

57\%

63\%

2 solutions

A Former Brilliant Member
Feb 22, 2021

You should really give the situation as the lies may not match sometimes( let’s say it’s a murder scene, one may say a boy in a black hoodie killed while the other says a boy in a blue hoodie killed but in reality a boy in a brown hoodie killed)

Jason Gomez - 3 months, 2 weeks ago

This is addressing their intention to tell the truth or lie. In the event they're telling the truth, they may still be unreliable in stating the facts although their intent is to tell the truth.

A Former Brilliant Member - 3 months, 2 weeks ago

Hmm.. ok, point accepted

Jason Gomez - 3 months, 2 weeks ago

@Jason Gomez – Nobody has solved "Chance Encounter at Restaurant" that we discussed. Any interest? Very curious as to why this problem seems to draw little interest.

A Former Brilliant Member - 3 months, 2 weeks ago

@Jason Gomez – Actually I feel the solution is wrong myself, in probability it’s most likely that neither go there for 20 days, it is not necessary that it will happen all the time, also it has to be mentioned that this is in a sample of 49 days, because if I take 98 days then most probably neither wouldn’t have gone to the restaurant on 40 days, so the wording needs to be changed. I didn’t notify this to you because there was already so much discussion about the problem, on how the wording should be changed that I didn’t feel like telling, cause that would confuse you more (I would be really confused if I had so many suggestions given to me)

Jason Gomez - 3 months, 2 weeks ago

@Jason Gomez – Thanks for your feedback. Think I'll take it down for now.

A Former Brilliant Member - 3 months, 2 weeks ago

@Jason Gomez – If you are making the same type of problem again, keep this trick in mind, 7 is most probable on a pair of dice, roll the dice 36 times and you are very likely to get 6 of them as 7 but not necessarily, you could very well get 12 sevens also!

Jason Gomez - 3 months, 2 weeks ago

@Jason Gomez – (Not required if this increases the confusion) The probability you get 6 sevens in 36 rolls works out to be 17.59%, the highest compared to getting 1 seven, 2 sevens … 5 sevens, 7 sevens… 36 sevens

Jason Gomez - 3 months, 2 weeks ago

Saya Suka
Apr 4, 2021

P(statements agree)
= (8/10)(5/7) + (1 – 8/10)(1 – 5/7)
= (4/5)(5/7) + (1/5)(2/7)
= (20 + 2) / 35
= 22 / 35
= 66 / 105
≈ 60% ~ 65%