IIT JEE , AIEEE Forum - Mathematics , Algebra

rockey

A speaks truth 75 %, B speaks truth 80%, what is the probability that both their statements donot match.

rates assured . i need explaination

sboosy

it is
1- P (both matching)
P(both matching)= P(truth (intersection)truth)
that is 3/4 * 4/5
so 1-3/5= 2/5
NOTE: two events being independent their intersection is the individual products

rockey

sboosy ans is given as 7/20
and it s iit 75 question

sboosy

yes it is possible for that also
see mayb they consider cases when both lie also
that case answer is what u say
u have to subtract that also isnt it
so 2/5- 25/100*20/100
exactly 7/20
BUT
my point is that
if they lie
they could lie in the same way!!!
anway if u include the answer is 7/20 (considering both lies )

rockey

sboosy can u be more clear why u have to subtract

sboosy

ya sure
1)when they both speak the truth their statements match
2)when they both lie their statements cud match or not match
this second one is in high ambiguity
if u consider that when they lie too they lie in the same way
again it becomes that they say the same thing
so this case becomes just like the first one 1)
so just like u subtract 1) u subtract 2) also

hsbhatt

I think the problem must be stated that it is known that a certain event E has taken place and A and B are only asked to report to someone that it has taken place. Given that A lies 75% etc...., what is the probability that their statements do not match.

Then our machiavellian sboosy will arrive at 7/20.

sboosy

Bhattji what do u mean by that?

Aatish

Let E is the event that A speaks truth...

then P(E) = 3/4

and let F is the event that B speaks truth....

then P(F) = 4/5

Then the event that their statements contradicts is denoted by ( E

F' )

( E'

F )

Then Required Probability is denoted by.....
P ( ( E

F' )

( E'

F ) ) = P ( E

F' ) + P( E'

F )

                                            = P (E).P(F') + P(E')P(F)

                                           = (3/4)(1/5) + (4/5)(1/4)

                                            = 7/20

Hope it is clear now..........

Cheerss!!!

hsbhatt

All I meant was that there will then be no chance of both lying in the same way or both speaking the truth but in different ways etc. That is lateral thinking man.

sboosy

How sure are u abt the fact Aatish that when they lie they lie in the same manner

hsbhatt

or when they speak the truth they say the same things?

cyborg

It can be done like this:

Cases in which the statements do not match are 3

1) A lies ,B speaks the truth

2)B lies ,A speaks the truth

3)A & B both lie.(Chances of them telling a lie in thr same way is very improbable)

So, the total prob

(1/4)*(4/5) + (3/4)*(1/5) + (1/4)*(1/5) = 7/20

Hope this makes it more clear,rockey

Aatish

Well I dont say this....Ques says it........

It says.....There Statements contradict.........which simply means if A tells truth B has to speak false..........and if A speaks false then B has to speak truth.........thats what I have denoted in Set Notation form....

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