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 requires the application of probability concepts, specifically the Bayes' theorem, to determine the likelihood of selecting a patient who needs surgery from the hospital admissions.
**Why the Correct Answer is Right**
Let's break down the problem step by step. First, we need to calculate the probability of a patient being a girl who needs surgery and a boy who needs surgery. We have 20 girls out of 50 admissions, and 10 of them need surgery, so the probability of a girl needing surgery is 10/20 or 1/2. Similarly, the probability of a boy needing surgery is 20/30 or 2/3. Now, we need to find the probability of picking up a person requiring surgery. We can use the law of total probability, which states that the probability of event A is the sum of the probabilities of event A occurring given that event B has occurred, times the probability of event B. In this case, event A is picking up a person requiring surgery, and event B can be either a girl or a boy.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it doesn't take into account the gender distribution of the patients. The probability of picking up a person requiring surgery depends on the gender of the patient.
**Option B:** This option is incorrect because it calculates the probability of a girl needing surgery, but doesn't consider the overall probability of picking up a person requiring surgery.
**Option D:** This option is incorrect because it calculates the probability of a boy needing surgery, but doesn't consider the overall probability of picking up a person requiring surgery.
**Clinical Pearl / High-Yield Fact**
When calculating probabilities in clinical scenarios, it's essential to consider the underlying population and the specific events being analyzed. In this case, the probability of picking up a person requiring surgery depends on the gender distribution of the patients and the probability of each gender needing surgery.
**Correct Answer: C. 0.4**