Solution
Question A:
- The theoretical probability is just the ideal probability of choosing a ball labeled 9 from 10 balls.
- This is gotten using the formula below
[tex]P(9)=\frac{\text{ Number of balls labeled 9}}{\text{Total Number of balls}}[/tex]- Thus, we can find the theoretical probability as follows
[tex]P(9)=\frac{1}{9}\approx0.111\text{ (To the nearest thousandth)}[/tex]Question B:
- The Experimental probability is the probability based on the experimental values gotten in trials.
- This probability is gotten by the formula below:
[tex]P_E(9)=\frac{\text{Number of trials that resulted in 9}}{\text{Number of trials in total}}[/tex]- The experimental probability is given
[tex]P_E(9)=\frac{6}{40}=0.150\text{ (to the nearest thousandth)}[/tex]Question C:
- The experimental probability should be equal to the ideal probability for consistency's sake. But many times, we get values not close to the theoretical probability in a few trials.
- But after a large number of trials, the experimental probability becomes more and more like the theoretical probability.
- Thus, the answer to this question is OPTION B
Final Answer
Question A
[tex]P(9)=\frac{1}{9}\approx0.111\text{ (To the nearest thousandth)}[/tex]Question B
[tex]P_E(9)=\frac{6}{40}=0.150\text{ (to the nearest thousandth)}[/tex]Question C
OPTION B