On a given day, a hospital had 50 admissions with about 20 girls and 30 boys, out of which 10 girls and 20 boys needed surgery. What is the possibility of picking up a person requiring surgery –
**Core Concept**
The question tests the understanding of conditional probability, specifically the concept of applying Bayes' theorem in a real-world scenario. Bayes' theorem is used to calculate the probability of an event, given some prior knowledge of conditions that might be related to the event.
**Why the Correct Answer is Right**
To calculate the probability of picking up a person requiring surgery, we need to consider the total number of patients requiring surgery (10 girls + 20 boys = 30) out of the total number of patients admitted (50). The probability of picking up a person requiring surgery is calculated by dividing the number of patients requiring surgery by the total number of patients admitted. However, the question asks us to consider the possibility of picking up a person requiring surgery given that we know they are a girl or a boy. We can use Bayes' theorem to calculate this conditional probability.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not take into account the number of girls and boys requiring surgery separately. We need to consider the conditional probability of picking up a person requiring surgery given that they are a girl or a boy.
**Option B:** This option is incorrect because it assumes that the probability of picking up a person requiring surgery is the same for both girls and boys, which is not the case.
**Option C:** This option is incorrect because it does not provide a clear calculation for the conditional probability.
**Option D:** This option is incorrect because it does not take into account the total number of patients admitted.
**Clinical Pearl / High-Yield Fact**
When applying Bayes' theorem in real-world scenarios, it's essential to consider the conditional probability of an event given some prior knowledge. This can be particularly useful in medical decision-making, where we often need to weigh the probability of different diagnoses or treatment outcomes.
**Correct Answer:** . The probability of picking up a person requiring surgery given that they are a girl is 10/20, and given that they are a boy is 20/30. The correct answer is not provided, but we can calculate it using Bayes' theorem: P(surgery|girl) = 10/20 / (10/20 + 20/30) = 10/20 / (3/10 + 2/3) = 10/20 / (9/30 + 20/30) = 10/20 / (29/30) = 10/20 * 30/29 = 3/4.8 = 0.625. Similarly, P(surgery|boy) = 20/30 / (10/20 + 20/30) = 20/30 / (3/10 + 2/3) = 20/30 / (9/30 + 20/30) = 20/30 / (29/30) = 20/30 * 30/29 = 2/4.8 = 0.4167.