Question

If you roll a number cube 60 times and use the results to calculate the experimental probability of rolling a 1, the experimental probability of rolling a 1 will ___ be less than the theoretical probability of rolling a 1.

Answer 1

Step-by-step explanation:

The experimental probability could be more, the same or less than the theoretical probability of rolling a 1 (which is 1/6).

The larger your sample (i. e., as you go beyond 60 tosses), the closer the two different probabilities are likely to be. (Think: Law of Large Numbers).

Answer 2

The experimental probability of rolling a 1 will likely be less than the theoretical probability of rolling a 1, but not always certainly.

Step-by-step explanation:

Theoretical probability: This is the probability of an event happening based on pure chance or equally likely outcomes. In the case of rolling a fair number cube, the theoretical probability of rolling a 1 is 1/6, as there is 1 favorable outcome (rolling a 1) out of 6 total possible outcomes.

Experimental probability: This is the probability of an event happening based on actual observations or experiments. In your scenario, the experimental probability would be calculated by dividing the number of times you roll a 1 by the total number of rolls (60).

While the theoretical probability remains constant at 1/6, the experimental probability can fluctuate due to random chance. However, as the number of rolls increases, the experimental probability tends to get closer to the theoretical probability. This is because the Law of Large Numbers states that as the number of random trials increases, the average of the results will approach the expected value or theoretical probability.

Therefore, while you are more likely to get an experimental probability lower than the theoretical probability due to random fluctuations, with enough rolls, the experimental probability will eventually get closer to the theoretical value of 1/6.

Here's an analogy: Imagine flipping a fair coin 10 times. You might get 7 heads and 3 tails, resulting in an experimental probability of heads being 7/10, which is higher than the theoretical probability of 1/2. However, if you flip the coin 1000 times, you're more likely to get closer to the theoretical probability of 1/2 for heads.

Remember, the key takeaway is that the theoretical probability represents the long-term average, while the experimental probability can vary due to random fluctuations in the short term.