could someone please give me an example not an example using coins, marbles, spinner, like something different that would explain the difference b/w theoretical and experimental probability.
And please explain.
Certainly! Let's use an example involving a deck of cards to explain the difference between theoretical and experimental probability.
Theoretical probability refers to the likelihood of an event occurring based on mathematical calculations and reasoning. It is determined by the number of favorable outcomes divided by the total number of possible outcomes. For instance, if you have a standard deck of 52 playing cards and you want to find the probability of drawing a heart, since there are 13 hearts in the deck, the theoretical probability would be 13/52, which simplifies to 1/4 or 25%.
Experimental probability, on the other hand, is determined through experimentation and real-world trials. It is based on the actual results obtained from conducting an experiment or repeated trials. In this case, you would physically draw cards from the deck and record the number of times you draw a heart out of a certain number of trials. For example, if you drew 100 cards and got 30 hearts, the experimental probability would be 30/100, which simplifies to 3/10 or 30%.
By comparing the theoretical and experimental probabilities, you can see if the observed results align with the expected outcomes. In this example, if the experimental probability of drawing a heart ends up being close to 25%, it suggests that the actual results align with the theoretical probability. However, if the experimental probability deviates significantly from the theoretical probability, it indicates that the results obtained through real-world trials differ from the predicted outcomes.