IIT JEE , AIEEE Forum - Mathematics , Algebra

m.viddya

Q.The odds that a book is reviewed favourably by 3 independent critics are 5:2,4:3 and 3:4 respectively.then the probability that out of 3 reviews,a majority will be favourable is?

m.viddya

well..the above problem comes under the conditional theorem of probability..can some help me out with it?

ramyadiamond

Probability of the 1st critic,say A,giving the review in favour is= P(A) = 5/5+2 =5/7

Probability of the 2nd critic, giving the review in favour = P(B) =4/4+3 =4/7

Probability of the 3rd critic giving the review in favour = P(C)= 3/3+4 =3/7

Now the review given by the each critic is independent of wat others have to say.

So the probability for the cases having majority of the reviews in favour can be in 4 ways.

1. When A,B are in favour and C is not

P₁ = (5/4) (4/7) .(1-3/7) = 80/343

2. When A,C are in favour but B is not :

P₂ =(5/4)(1-4/7)(3/7) = 45/343

3. When B,C are in favour and A is not

P₃ =(1-5/7)(4/7)(3/7) = 24/343

4. When all three are in favour:

P₄ =(5/7) (4/7) (3/7)= 60/343

So the total probability of getting the reviews in favour is

P₁ +P₂ +P₃ +P₄ =209/343

Hope u got it!!!

Cheerss!!!

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