can someone help me with this word problem

Question

If joe flips a coin 20 times and gets 12 heads He concludes that the probability of getting a head is .60 or 60%. Is this a theoretical probability or experimental probability? Explain your answer 

Answer 1

This is experimental probability.

 

Experimental probability is defined as the total number of times an event occurs divided by the total number of trials. In this instance, 12/20=.60 or 60%. So that would be the total times an event occurs (getting heads) divided by the total trials (20 flips).

 

Theoretical probability is defined as the total number of events one wants to observe divided by the total number of outcomes. This is a little more abstract to understand. Put into context of this situation, there is only one event joe wants to observe (getting heads). He is only observing the amount of times he gets heads so he is only observing one event. However, there are two possible outcomes every time he flips the coin (it can land on heads or tails). Therefore, there is one event he wants to observe and two possible outcomes of every flip. so 1/2=.5 or 50%.

 

Theoretical outcome is basically how many times something "should" happen. If you think about a coin flip, all other things equal, you should get heads half the time because heads represents one half of the possible results of the flip.

 

TL;dr the answer is experimental probability. He did an experiment to get his result and divided number/number of trials or events/trials.