Answer:
The experimental probability of throwing a five is 0.087.
Step-by-step explanation:
Given:
Number of trials (n) = 100
Number of times 5 appears (x) = 14
Let the event of occurrence of 5 be success and the probability represented by 'p'. So, all the other numbers occurrence is failure and its probability is represented as 'q'.
Probability of success is given as:
![p=\frac{Number\ of\ favorable\ events}{Total\ number\ of\ outcomes}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7BNumber%5C%20of%5C%20favorable%5C%20events%7D%7BTotal%5C%20number%5C%20of%5C%20outcomes%7D)
Favorable event is occurrence of 5. So, its number is 1 as there is only one 5 in the die. Total outcomes are 6 as there are six numbers. So,
![p=\frac{1}{6}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B1%7D%7B6%7D)
Now, probability of failure is given by the formula:
![q=1-p=1-\frac{1}{6}=\frac{5}{6}](https://tex.z-dn.net/?f=q%3D1-p%3D1-%5Cfrac%7B1%7D%7B6%7D%3D%5Cfrac%7B5%7D%7B6%7D)
Now in order to find the experimental probability of 14 successes out of 100 trials, we apply Bernoulli's theorem which is given as:
![P(x) = ^nC_xp^xq^{n-x}](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%5EnC_xp%5Exq%5E%7Bn-x%7D)
Plug in all the given values and find the probability of 14 successes. This gives,
![P(x=14)=^{100}C_{14}(\frac{1}{6})^{14}(\frac{5}{6})^{100-14}\\\\P(x=14)=0.087](https://tex.z-dn.net/?f=P%28x%3D14%29%3D%5E%7B100%7DC_%7B14%7D%28%5Cfrac%7B1%7D%7B6%7D%29%5E%7B14%7D%28%5Cfrac%7B5%7D%7B6%7D%29%5E%7B100-14%7D%5C%5C%5C%5CP%28x%3D14%29%3D0.087)
Therefore, the experimental probability of throwing a five is 0.087.