Empirical Probability Examples
Example 1. You have conducted a taste test of 100 people that reveals 65 people prefer apple and the remaining prefer banana. Find the empirical probability a person prefers apple over the banana?
Solution:
P(H) = Number of times an event occurred / Total number of trails
P(H) = 65 / 100 = 0.65
The empirical probability of person preferring apple over banana is 0.65
Example 2. A coin is tossed 5 times and all the three times head showed up. What is the empirical probability of showing a tail when the coin is tossed?
Solution:
P(H) = Number of times an event occurred / Total number of trails
P(H) = 0 / 5 = 0
The empirical probability of getting a tail is 0.
Example 3. A coin is tossed 2 times and all the three times head showed up. What is the empirical probability of showing a head when the coin is tossed?
Solution:
P(H) = Number of times an event occurred / Total number of trails
P(H) = 2 / 2 = 1
The empirical probability of getting a head is 1
Example 4. In a dinner for which 120 people attended, 80 people preferred mushrooms and others preferred panners. What is the empirical probability of a person to choose mushroom?
Solution:
P(H) = Number of times an event occurred / Total number of trails
P(H) = 80 / 120 = 2 / 3 = 0.67
The empirical probability of a person to choose mushroom is 0.67
Example 5. A dice is tossed 10 times and the recordings are recorded in the following table.
| Outcome | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Frequency | 3 | 2 | 0 | 1 | 3 | 1 |
Find the probability of getting a number 4 when the dice is thrown?
Solution:
P(H) = Number of times an event occurred / Total number of trails
P(H) = 1 / 10 = 0.1
The empirical probability of getting a number 4 when dice is tossed is 0.1
Example 6. There are four marbles in a box and they are of distinct colors red, yellow, green, and blue. One ball is picked each time and this is done 40 times. The observations are recorded in the following table.
| Outcome | Red | Yellow | green | blue |
|---|---|---|---|---|
| Frequency | 15 | 12 | 6 | 7 |
Find the probability of getting a blue ball when a ball is drawn at random?
Solution:
P(H) = Number of times an event occurred / Total number of trails
P(H) = 7 / 40 = 0.175
The empirical probability of getting a number blue ball is 0.175
Empirical Probability
Empirical Probability: Probability describes the chance that an uncertain event will occur. Empirical probability is based on how likely an event has occurred in the past. It is also called experimental probability. It is based on the relative frequency approach. We can get our results from experience rather than from a theory.
We employ the empirical probability-generating function in constructing a goodness-of-fit test for negative binomial distributions. In empirical probability, the experimental conditions may not remain the same for all repetitions of that experiment. In statistical terms, the empirical probability is just an estimate of an event.
Table of Content
- Empirical Probability Meaning
- Difference Between Empirical Probability and Theoretical Probability
- Empirical Probability Examples
- Advantages of Empirical Probability
- Disadvantages of Empirical Probability
- Summary – Empirical Probability
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