# Experimental Probability Examples in Real Life

Experimental probability is the results from an actual experiment of repeated trials. In class, examples are sometimes given with coin tosses or dice rolling. For example, you could toss a coin 50 times to see the probability of getting heads (your results should come close to the theoretical probability of 0.5). While these can serve as a great starting point for understanding experimental probability, there is abundance of experimental probability examples in real life.

## 6 Experimental Probability Examples in Real Life

• Business: A cake shop owner wants to know what fraction of sales will be his new gluten free cupcake line. He tallies the products sold on the first day of the week (60 regular and 40 gluten free) and finds that 40/100 = 4/10 = 2/5 of his weekly sales will probably be gluten free cupcakes.
• Farming: A vegetable grower wants to know the probability a new strawberry seed will sprout. He sows 1,000 seeds and finds that 829 sprout. The experimental probability is 829/100.
• Sports: A baseball manager wants to know the probability a potential new player has of hitting a home run in his first at bat for any game. Historically, the player has hit 21 home runs in 2,925 games. The probability he will hit a home run in his first at bat is 21/2925 = 0.007179 or .7179%.
• Weather forecasting: It rained 12 days in March (a probability of 12/31). Using this information, you predict that the probability the number of rainy days next March is 12/31.
• Extreme event forecasting: The law of large numbers tell us that if we repeat an experiment over and over again, experimental probability will approach the true probability. This law is very useful for making predictions, like the probability of a hurricane hitting Florida after October 1st every year (1 out of 3) [1], or the probability of an eruption occurring within the next thirty years in California—16% according to past data [2].
• Politics: A polling company wants to know how many people are in favor or raising the debt ceiling and how many people are against it. A few random people are selected (this is called a sample space) and their answers are 61% for an 39% against. This data is used to estimate that 61% of people in the U.S. will be for the measure.