Question

A proper unbiased coin was tossed 10 times for 3 trials, giving TTHHTHTTHH, TTTTTHHHHH, and THTHHHTTH (T = Tails; H = Heads). What is the difference between the theoretical and experimental probabilities of getting heads?

Answer 1

The answer is A. (0.0) for Plato/Edmentum.

Explanation:

Theoretical Probability:

There are only two possible outcomes, heads or tails. So the theoretical probability is ....

1/2 = .5 x 100 = 50%

Experimental Probability:

So in order to find the experimental probability you need to find out how many outcomes were heads and the total number of tries. So lets make this as simple as possible...

1 2 3 4 5 6 7 8 9 10 <---- Number of tries

T T H H T H T T H H <----- T = 5 , H = 5

1 2 3 4 5 6 7 8 9 10 <------ Number of tries

T T T T T H H H H H <------- T = 5 , H = 5

1 2 3 4 5 6 7 8 9 10 <------- Number of tries

T H T H H H T T H T <------- T = 5 , H = 5

Now that we know all the information we can use it to find the experimental probability. Theres a total of 15 outcomes that were heads and a total of 30 tries, so let's calculate....

15/30 = .5 x 100 = 50%

Summary:

Now hopefully you can see that .5 - .5 = 0.0, So the CORRECT answer is

A. 0.0

Answer 2

The theoretical probability will remain the same every time you do the experiment (50%), while the experimental probability will vary somewhat, since you probably aren't going to get 5 heads every single time.