What is the experimental and theoretical probability??? (read description)

Question

I flipped an even coin 100 times.

I recorded the results of each coin toss in a table.

Two heads 35
Two tails 23
One head, one tail 52

 

1. What is the theoretical probability that a coin toss results in two heads showing?
2. What is the experimental probability that a coin toss results in two heads showing?
3. What is the theoretical probability that a coin toss results in two tails showing?
4. What is the experimental probability that a coin toss results in two tails showing?
5. What is the theoretical probability that a coin toss results in one head and one tail showing?
6. What is the experimental probability that a coin toss results in one head and one tail showing?
7. Compare the theoretical probabilities to your experimental probabilities. Why might there be a difference?

 

PLEASE HELP AND ANSWER ASAP

Answer 1

Theoretical probability is based on the likelihood of events.  It is the ratio of successes to the total number of cases.  For flipping a coin once, the theoretical probability of it coming up heads is .5 and the probability of it coming up tails is .5 (assuming it will never land on its edge and stay that way).

 

The problem statement must mean “tossing a coin twice” or “tossing two coins.”  Which did you do in your experiment??

So, let’s enumerate (list all the equally-likely cases) that can occur with two coins:

   HH
   HT
   TH
   TT
 
The probability (likelihood) of getting two heads is 1 in 4  (.25).  The likelihood of getting two tails is also 1 in 4 (.25).  However, the likelihood of getting one head and one tail (in any order) is 2 in 4  (.5).

Note:  the probability of a coin flip does not depend on what has happened in previous flips; this is very important !!

 

An experiment may differ from this theoretical probability for a number of reasons:  The coin might actually not be “fair,” you may have a flipping technique that favors one result (if so, you might want to become a gambler), …  

 

Although experimental probability may differ from theoretical probability, it should not be too much different (note:  we could express the probability that it will be 10% off, 20% off, etc.).