Question

50 POINTS!!!!!!

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?

The experimental probability is_______ , which is the theoretical probability of________ .

Choices= 1/12, 1/6, 1/4, 1/3, 1/2, greater than, less than, equal to

Answer 1

Answer:
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.
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Step-by-step 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:


`(1)/(2) * (1)/(2) = (1)/(4)`

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.