# Probabality question involving conditional probabality

• laurenkinnaly
No, in this context, surviving refers to the patient being alive after the operation. So if the body rejects the organ, the patient does not survive.
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?

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.)

laurenkinnaly said:
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)

╔(σ_σ)╝ said:
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?

statdad said:
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" ?

## 1. What is conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is denoted as P(A|B), which reads as "the probability of event A happening given that event B has occurred."

## 2. How is conditional probability calculated?

Conditional probability is calculated by dividing the probability of the intersection of two events by the probability of the given event. This can be represented as P(A|B) = P(A ∩ B) / P(B).

## 3. Can you give an example of a conditional probability question?

One example of a conditional probability question is: "If a fair six-sided die is rolled twice, what is the probability of getting two even numbers given that the first roll was a multiple of 3?"

## 4. What is the difference between conditional probability and regular probability?

The main difference between conditional probability and regular probability is that conditional probability takes into account additional information, such as the occurrence of another event, to calculate the likelihood of an event. Regular probability does not consider any additional information and is simply calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

## 5. How is conditional probability used in real life?

Conditional probability is used in various fields such as economics, medicine, and data analysis. For example, in medicine, conditional probability is used to determine the likelihood of a patient having a certain disease given their symptoms and medical history. In data analysis, conditional probability is used to predict customer behavior based on their past purchases and demographic information.

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