Distribución binomial (Ejercicio resuelto)
Probability Calculation in a Hospital Scenario
Introduction to the Problem
- The video introduces a probability exercise involving an event with a 55% chance of occurring each time someone enters a hospital. The goal is to determine the probability that this event occurs for 2 out of 5 people entering today.
Defining Variables
- The probability of the event occurring is denoted as p, which equals 0.55 (converted from 55%).
- The probability of the event not occurring is denoted as q, calculated as 1 - p, resulting in q = 0.45.
Experiment Setup
- To perform calculations, percentages are expressed in decimal form: p = 0.55 and q = 0.45.
- Two additional variables are defined: n (the total number of trials, which is 5 for five people entering the hospital) and X (the number of successful occurrences we want to find, which is set at X = 2).
Using Binomial Distribution Formula
- With p, q, n, and X established, the video explains how to use the binomial distribution formula to calculate probabilities.
- The formula requires substituting values: n = 5, x = 2, p = 0.55, and q = 0.45.
Calculating Coefficients
- The binomial coefficient can be represented as "5 choose 2" or C(5,2) , calculated using factorial notation.
- Factorials are explained: n! means multiplying all positive integers up to n; thus C(5,2) simplifies through cancellation during calculation.
Final Probability Calculation
- After calculating C(5,2)=10 , raising p and q to their respective powers yields results needed for final multiplication.
- Ultimately, the computed probability that the event occurs for exactly two out of five individuals is approximately 0.2756, or about 27.565% when converted into percentage form.
Conclusion