EVENTOS INDEPENDIENTES probabilidad ejercicios resueltos
Understanding Independent Events in Probability
Introduction to Independent Events
- The video revisits the concept of independent events, emphasizing its importance and simplicity.
- Independent events occur when the outcome of one event does not affect the outcome of another. Classic examples include flipping coins or unrelated probabilities like sports scores and product purchases.
Calculating Probabilities of Independent Events
- To find the probability of two independent events occurring together, multiply their individual probabilities.
- For instance, if the probability of getting heads on a coin flip is 0.5, then for two flips, it’s calculated as 0.5 * 0.5 = 0.25.
Practical Examples
- An example involves calculating the probability that a soccer team scores a goal (20%) while simultaneously purchasing a specific brand of tuna (50%). The combined probability is 0.2 * 0.5 = 0.1 or 10%.
Formula Representation
- The formula for calculating joint probabilities of independent events is represented as P(A and B) = P(A) * P(B), where A and B are independent events.
Example with Colored Balls
- A scenario with three green balls, two white balls, and five red balls illustrates how to calculate probabilities when drawing from a set without replacement.
- The individual probabilities are: P(green)=3/10, P(white)=2/10, P(red)=5/10; thus for drawing one ball of each color: (3/10)(2/10)(5/10)=30/1000 or 3%.
Dice Rolling Example
- When rolling a die twice to get the number three both times, each roll has a probability of 1/6; hence combined it’s (1/6)*(1/6)=1/36.
- This results in an average occurrence rate where one would expect to roll two threes once every thirty-six attempts.
Conclusion on Independent Events
- The key takeaway is that for independent events, simply multiply their individual probabilities to find the overall likelihood of both occurring together.