Question

Design a probability experiment to determine the empirical probability of tossing two heads with two coins. Why might results be different from theoretical probability and how can the experiment be altered so that the theoretical and empirical results become equal?

Design a probability experiment to determine the empirical probability of rolling a 2 or a 5 with one die.Why might the results be different from theoretical probability and how can the experiment be altered so that the theoretical and empirical results become equal?

Answer 1

When asked about the probability of a coin landing on heads, you would probably answer that the chance is ½ or 50%. $theoretical_vs_img1.png$
Imagine that you toss that same coin 20 times. How many times would you expect it to land on heads? You might say, 50% of the time, or half of the 20 times. So you would expect it to land on heads 10 times. This is the theoretical probability.

The theoretical probability is what you expect to happen, but it isn't always what actually happens. The table below shows the results after Sunil tossed the coin 20 times.


This shows the experimental probability You can think of it as the probability determined from the results of an Outcomes Frequency Heads 13 experiment. It is what actually happens instead of what you were expecting to happen. Tails Total 20

The experimental probability of landing on heads is
13-65 = 0.65-65%. 20 100


It actually landed on heads more times than we expected.

Now, Sunil continues to toss the same coin for 50 total tosses. The results are shown below.


Outcomes Frequency Heads 26 24 Tails Total 50


Now the experimental probability of landing on heads is
26-52 = 0.52 0 100 52%


The probability is still slightly higher than expected, but as more trials were conducted, the experimental probability became closer to the theoretical probability.

Examples:

1. If you tossed 2 coins simultaneously for 4 times theoretical probability of getting 2 heads is 1/4th that is 25%. But practically there may be no appearance of two heads that is 0% or all four times you may get chance of getting two heads all the time that is 100%. So that is the difference between theoretical and practical probability.

2. Use the table below to determine the probability of each number on a number cube.

a. Rolling a 3 (use the table) -0.22 22% 100 Outcome Frequency b. What is the theoretical probability of rolling a 3? 16 20 -0.166666 6 * 17% c. Rolling a number less than 3 (use the table) 4 10 (Rolling a 1 or 2) 36-0.36-36% 100 18 14 d. Rolling a 3 or a 5(use the table) 100 Total 40 -0.40 40% 100