Question

Taka conducts an experiment where he rolls a number cube, with sides labeled from 1 to 6, and then flips a coin. This table shows the results from 12 trials.
Results 1 H -- 4 T -- 1 H -- 5 T -- 2 H -- 3 T -- 6 T -- 2 H -- 3 T -- 5 T -- 3 H -- 4 T

How do the experimental probability and theoretical probability of rolling an even number and then flipping a head in Taka's trials compare?

Give the values or phrases to correctly complete the sentence. The experimental probability is (?) , which is (?) the theoretical probability of (?).

Answer Choices - 1/12, 1/6, 1/4, 1/3, 1/2, Greater than, Less than, Equal too.

Answer 1

The experimental probability is 1/6, and the theoretical probability is 1/4. The theoretical probability is greater than the experimental probability in this trial.-------------------Explanation:
Theoretical probability is the mathematically calculated probability of the circumstances occurring. 
There is a 1/2 chance of rolling an even number, and a 1/2 chance of flipping a coin on heads.
Since the question asks for the possibility of both happening, multiply those together to find the probability:


The theoretical probability of rolling an even number and then flipping a head is 1/4.
Now we'll focus on Taka's trials.
Experimental probability is the probability that is taken from results of a trial.
Take the results, and see if they match the criteria of rolling an even number and flipping heads.
The results that are bolded fit the criteria:1 H, 4 T, 1 H, 5 T, 2 H, 3 T, 6 T, 2 H, 3 T, 5 T, 3 H, 4 T
Taka managed to roll and flip the coin to fit the criteria 2 times out of 12. Converted into a fraction, it is 2/12. Simplified, the experimental probability is 1/6