The probability of getting a bad apple in a lot of 5000 is 0.025. Find the number of bad apples in this lot.

Appeared in: KGMU 2023

Explanation

The question asks for the expected number of bad apples in a given lot, which is a direct application of probability.
The formula to find the expected number of an event is to multiply the total number of items by the probability of that event.
In this case, the total number of apples is 5000, and the probability of an apple being bad is 0.025.
The calculation is: 5000 × 0.025 = 125.
Therefore, the expected number of bad apples in the lot is 125.

Option A: This result is incorrect because it assumes a probability of 0.02 (100 ÷ 5000), not the given probability of 0.025.
Option C: This result is incorrect because it assumes a probability of 0.035 (175 ÷ 5000), not the given probability of 0.025.
Option D: This result is incorrect because it assumes a probability of 0.01 (50 ÷ 5000), not the given probability of 0.025.

Visual 1: Infographic - A simple graphic showing a large basket labeled '5000 Apples'. A smaller, separate group of 125 apples is shown with a label 'Bad Apples (2.5%)', visually representing the calculation 5000 x 0.025 = 125.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating Expected Value in Probability as background academic context rather than a clinical decision trigger.
While this is a math question, understanding probability is fundamental in healthcare for interpreting research, understanding risk factors, and evaluating the likelihood of treatment success or adverse events in a patient population.
For example, if a clinical trial reports that a side effect has a probability of 0.025, a nurse can anticipate that in a group of 5000 patients, about 125 might experience that side effect.
What if the probability was given as a percentage, like 2.5%? The first step is always to convert the percentage to a decimal by dividing by 100 (2.5 / 100 = 0.025) before performing the multiplication.

How to Approach the Question

First, identify the key information provided in the question: the total number of items (5000 apples) and the probability of a specific outcome (0.025 for a bad apple).
Recall the formula for calculating the expected number of an event: Expected Number = Total Count × Probability of the event.
Substitute the given values into the formula: Expected Number = 5000 × 0.025.
Perform the multiplication. A simple way to calculate this is to convert the decimal to a fraction: 0.025 = 25/1000. So, the calculation becomes 5000 × (25/1000).
Simplify the fraction: 5000/1000 = 5. The calculation is now 5 × 25, which equals 125.
Finally, compare your calculated answer (125) with the given options to find the correct choice.

Concept Tested & Keywords

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Practise the full KGMU 2023

Attempt every question from this paper in a timed mock, then review the full solution for each one.