Investigation 1 accessed blog

 By: Alyssa A.
Date: April 23, 2014
Block: F

1. How you would find the experimental probability is by completing trials. Theoretical probability is the number you get when you calculate how many times an outcome should show up. Experimental probability is the probability of those results (of the trials) once they are completed. If you were flipping a fair coin one side would show up about half the time.  As an example, you decide to flip one fair coin many times to find out what the probability is that you get heads. First you calculate the theoretical probability, which is 50 percent of the time you will get heads. You then complete 30 trials. Out of the 30 trials 16 are heads and 14 are tails. The favorable outcome ,14, over the number of outcomes ,30, equals 54 percent. Your trials therefore shows an experimental probability of 54 percent of the time that heads will come up. 54 percent and 50 percent are close together. If you had done more trials you would have come up, consistently, with 50 percent which is the spot on answer. If 34 percent of the time heads come up you would know that more trials would need to be conducted or that your theoretical probability was wrong. But since they are close to each other we now know that our theoretical probability is correct, as well as our experimental probability.

2. In experiments/trials 30 trials are not as good as 500 trials to prove your theoretical probability. 30 trials may bring you close to your theoretical probability, 500 however will bring you closer. Lets say you flip a fair coin and both times you get tails. Does that mean you will have a hundred percent chance (certain chance) that you will always get tails? No. If you flip a coin 30 times and track the outcomes down on a piece of paper, your probability of getting heads half the time would start to show up more. The coin has a theoretical probability of 50 percent of the time it being heads and 50 percent of the time being tails. Lets say your 30 trials show 13 heads and 17 tails. The favorable outcome of heads ,13, over the total number of outcomes , 30, equals 44 percent. Meaning that 44 percent of the time you got heads. However if you did a trial of 500 flips and you got 251 heads and 249 tails. The favorable outcome of heads , 251, over the total number of outcomes , 500, equals 50 percent. Meaning that 50 percent of the time you got heads. Doing more trials gives you a more accurate experimental probability that is closer to your theoretical probability. 

3. What it means for a chance to be equally likely is that your chances half of the time you will get one answer and the other half of the time you will get the other answer. To describe an equally likely chance a coin is the most common and best situation to describe this is a coin. So an equally likely probability would be a 50/50 chance. When you flip a coin you have an equally likely chance to get a head or a tails. Even though you flip a coin twice it does not mean you will absolutely get a head and a tail. There are many ways the coin trials could have. It could be head/head, tail/tail, head/tail, and tail/head. For a chance does not mean it will definitely happen, it means it’s what’s most likely to happen. You have the most likely chance of getting a head or a tail.

As we conducted more trials our numbers became more accurate. In the first few trials we were looking at a range between 60 - 100 percent. After 20 more trials we were looking at a range of 52 - 54 percent which is more confident and closer to the answer (50 percent).