Answer :
To determine the type of probability represented by obtaining eleven heads in twenty tosses of a fair coin, we can analyze the situation step-by-step.
1. Definition of Experimental Probability: Experimental probability refers to the likelihood of an event occurring based on the actual results of an experiment. It is calculated using the formula:
[tex]\[ \text{Experimental Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}} \][/tex]
2. Definition of Theoretical Probability: Theoretical probability, on the other hand, is based on the expected outcomes derived from a mathematical model or knowledge about the process. For a fair coin, the theoretical probability of getting heads in any single toss is 0.5 (or 50%).
3. Given Information: In this problem, we performed an experiment by tossing a fair coin 20 times and obtained 11 heads.
4. Calculation: The fraction representing this outcome is given by:
[tex]\[ p = \frac{Number \, of \, Heads}{Total \, Number \, of \, Tosses} = \frac{11}{20} \][/tex]
5. Interpretation:
- Since [tex]\( \frac{11}{20} \)[/tex] represents the ratio of the number of heads observed to the total number of tosses in an actual experiment, this ratio is an example of experimental probability.
- Theoretical probability remains constant at 0.5 for each toss of a fair coin but does not depend on the outcomes of the specific experiment conducted.
Therefore, the probability [tex]\( p = \frac{11}{20} \)[/tex] is an experimental probability because it is derived from the results of an actual experiment (the twenty coin tosses resulting in eleven heads).
1. Definition of Experimental Probability: Experimental probability refers to the likelihood of an event occurring based on the actual results of an experiment. It is calculated using the formula:
[tex]\[ \text{Experimental Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}} \][/tex]
2. Definition of Theoretical Probability: Theoretical probability, on the other hand, is based on the expected outcomes derived from a mathematical model or knowledge about the process. For a fair coin, the theoretical probability of getting heads in any single toss is 0.5 (or 50%).
3. Given Information: In this problem, we performed an experiment by tossing a fair coin 20 times and obtained 11 heads.
4. Calculation: The fraction representing this outcome is given by:
[tex]\[ p = \frac{Number \, of \, Heads}{Total \, Number \, of \, Tosses} = \frac{11}{20} \][/tex]
5. Interpretation:
- Since [tex]\( \frac{11}{20} \)[/tex] represents the ratio of the number of heads observed to the total number of tosses in an actual experiment, this ratio is an example of experimental probability.
- Theoretical probability remains constant at 0.5 for each toss of a fair coin but does not depend on the outcomes of the specific experiment conducted.
Therefore, the probability [tex]\( p = \frac{11}{20} \)[/tex] is an experimental probability because it is derived from the results of an actual experiment (the twenty coin tosses resulting in eleven heads).
