Huh?

Algebra Level 3

A speaks truth in 75% of the cases and B in 80% of the cases. In what % of cases are they likely to contradict each other in stating the same fact? The answer will come in the form of a/b when simplified. Kindly enter the value of a-b.

Note: Your answer will be negative since a < b.


The answer is -13.

Subhag Gupta by Subhag Gupta , 22, India

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3 solutions

Saya Suka
Mar 18, 2021

P(contradictory)
= (3/4)(1 - 4/5) + (1 - 3/4)(4/5)
= 3/20 + 4/20
= 7/20
= 35%

Answer = 7 - 20 = -13

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I guess we have to assume that the lie will always be the same, because otherwise we would need to consider the case in which they both lie.

Tristan Goodman - 2 months, 2 weeks ago

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Since we're not told how creative these two could be, I just took it as they're posed with a yes-no binary questions and answered accordingly (also assuming they both know all the true facts in the first place), but I totally agree that they both can still be contradictory with 2 lies (the truth is X but A may choose to tell Y while B telling Z) if given just another degree of freedom even with just 3 possible replies.

Saya Suka - 2 months, 2 weeks ago
Ramiel To-ong
May 21, 2015

first case they will contradict: A will lie and B will not = 0.25(0.80) = 1/5 second case they will contradict: B will lie and A will not = 0.20(0.75) = 3/20 sum of the total = 7/20 a - b = 3-20 = -13

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Here have some mistake, not 3 - 20 = -13 , it will 7 - 20 = -13.

Shohag Hossen - 6 years ago

here have seen some mistake, not 3 - 20 = -13 , it will 7 - 20 = -13.

Am Kemplin - 1 month, 3 weeks ago

of course a\b is wrong. so. it's gotta be 50.

Am Kemplin - 1 month, 3 weeks ago
Abhijeet Verma
May 9, 2015

The two cases can be when A speaks truth and B speaks false , and when A speaks false and B speaks truth. Adding the two probabilities, we get a/b.

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