Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • In a certain town, there are two hospitals, Hospital A and Hospital B, which serve the population. It is known that 60% of the population visits Hospital A, 40% visits Hospital B, and 20% visits bo

In a certain town, there are two hospitals, Hospital A and Hospital B, which serve the population. It is known that 60% of the population visits Hospital A, 40% visits Hospital B, and 20% visits both hospitals. Suppose a person is selected at random from the population. What is the probability that this person visits Hospital A, given that they have visited Hospital B?

Option: 1

0.2


Option: 2

0.5


Option: 3

0.7


Option: 4

0.8


Answers (1)

best_answer

We can use Bayes' theorem to solve this problem. 

Let A be the event that a person visits Hospital A, and B be the event that a person visits Hospital B. 

We want to find the probability of A given that B has occurred, which is written as P(A|B). 

We know that 20% of the population visits both hospitals, so the probability of visiting both hospitals is: 

P(A and B) = 0.2

We also know that 60% of the population visits Hospital A, so the probability of visiting Hospital A is: 

P(A) = 0.6 

Now, we know that 40% of the population visits Hospital B, so the probability of visiting Hospital B is: 

P(B) = 0.4

Finally, we want to find the probability of visiting Hospital A given that the person has visited Hospital B, which is P(A|B).

Using Bayes' theorem, we can write:

{P(A/B)=\frac{P(B/A)\times P(A)}{P(B)}}

We need to find P(B|A), the probability that the person visits Hospital B, given that they have visited Hospital A. We can use the formula for conditional probability:

{P(B/A)=\frac{P(A \ \text{and}\ B)}{P(A)}}

Substituting the given values, we get:

\\{P(B/A)=\frac{0.2}{0.6}}\\ \\\Rightarrow {P(B/A)=\frac{1}{3}}

Finally, we can substitute these values into Bayes' theorem to find P(A|B):

\\{P(A/B)=\frac{\frac{1}{3}\times 0.6}{0.4}}\\ \\\Rightarrow {P(A/B)=\ 0.5}

Therefore, the probability that a person visits Hospital A, given that they have visited Hospital B, is 0.5.

Posted by

Rakesh

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today
anam-khan

JoSAA round 2 cut-off 2025 out; BTech closing ranks for top engineering courses at IITs
anam-khan

Goa Engineering Admission 2025: 1,415 eligible for BE seats; merit list on June 27

Latest Question