How to Find Experimental Probability?
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Experimental probability is determined by carrying out a probability experiment and recording the number of times an event occurs. It gives us a practical perspective on the likelihood of an event.
Steps to Find Experimental Probability:
- Conduct the Experiment:
Perform the probability experiment a certain number of times. This number is referred to as the total number of trials, represented by \( n \).
- Record the Outcomes:
Take note of how many times the event of interest occurs. This is termed as the number of successful outcomes, represented by \( s \).
- Calculate the Experimental Probability:
Use the formula: \[ P(E) = \frac{s}{n} \] where \( P(E) \) is the experimental probability of event \( E \), \( s \) is the number of successful outcomes, and \( n \) is the total number of trials.
Example:
Suppose you roll a dice 50 times and the number 4 appears 8 times. What's the experimental probability of getting a 4?
Solution:
Here, \( n = 50 \) (since the dice is rolled 50 times) and \( s = 8 \) (as the number 4 appeared 8 times).
Using the formula: \[ P(E) = \frac{s}{n} \] \[ P(4) = \frac{8}{50} = \frac{4}{25} = 0.16 \]
So, the experimental probability of getting a 4 when rolling the dice is 0.16 or 16%.
Note:
Experimental probability offers an empirical method to determine the likelihood of an event based on actual trials. By comparing experimental and theoretical probabilities, we can analyze the behavior of random phenomena more comprehensively.
