What happens to the theoretical probability and the experimental probability as the sample space increases?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The theoretical probability remains unchanged as the size of the sample space changes in any direction. For example, if you flip a fair coin the probability of getting heads is one half for every flip. Thus we expect one half of all flips to land on heads whether there is...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

The theoretical probability remains unchanged as the size of the sample space changes in any direction. For example, if you flip a fair coin the probability of getting heads is one half for every flip. Thus we expect one half of all flips to land on heads whether there is 1 flip, or there are hundreds of flips.

By the law of large numbers, we expect the experimental probability to approach the theoretical probability as the sample space gets larger. For example, if you flip a coin 10 times and get 6 heads, then the experimental probability of getting heads is 0.6. As the number of trials increases, thus increasing the sample space, the number of heads should approach the theoretical probability of 0.5. This assumes that we are correctly flipping a fair coin. Note that if the experimental probability does not get close to the theoretical probability, this might indicate an unfair coin or improper technique.

Approved by eNotes Editorial Team