Probabality question involving conditional probabality

[laurenkinnaly]

The probability of surviving a certain operation is .55. If a patient survives the operations, the propability that his or her body will reject the transplant within a month is .20. What is the probability of surviving both these critical stages.

I am going to say P(A) = .55 and P(B | A ) = .20

They want to know what is the probability that P(A and B) right?

So, P(B | A) = P(A and B) / P(A)
so P(A) * P(A|B) = P( A and B) .
so P(A and B) = .55(.20) = .11. But the answer in the back of my book is saying .44

Can someone explain why I am not getting the right answer?

 

[statdad]

The key phrase is " surviving both of these critical steps".

What, exactly, does $P(B | A) = 0.20$ the conditional probability of? (Say it in words and see if it is the value you want to use.)

 

[╔(σ_σ)╝]

So, P(B | A) = P(A and B) / P(A)
so P(A) * P(A|B) = P( A and B) .

First of all, the part in bold is incorrect.

You put P(A|B) = P(B|A)

 

[statdad]

First of all, the part in bold is incorrect.

You put P(A|B) = P(B|A)

It would seem to be a typo by the OP, as the original numbers created were used with the original meaning.

The question is still: is it $0.20$ that should be used?

 

[╔(σ_σ)╝]

It would seem to be a typo by the OP, as the original numbers created were used with the original meaning.

The question is still: is it $0.20$ that should be used?

Okay.@laurenkinnaly

If the persons body rejects the organ does he/she "survive" ?