John tosses a penny 10 times and finds that 2 of those times the penny comes up heads and 8 of those times the penny comes up tail. What should John conclude?
a.That the expected relative frequency probability of getting heads when tossing a penny is 2/10.
b. That it is more probable to get tails than it is heads when tossing a penny
C. That in the long term, the expected relative frequency would be 5/10. Because he has only tossed the penny 10 times, a different pattern has emerged.
What do you think the answer is, Mike?
Right.
To answer this question, we need to understand the concept of relative frequency probability. Relative frequency probability is a measure of how likely an event is to occur based on the frequency in which it occurs relative to the total number of trials.
In this case, John tossed the penny 10 times and obtained the following results: 2 heads and 8 tails. To find the relative frequency probability of getting heads, we divide the number of times heads occurred by the total number of trials.
Therefore, the relative frequency probability of getting heads in John's experiment is 2/10, which simplifies to 1/5.
Now let's analyze the answer choices:
a. "That the expected relative frequency probability of getting heads when tossing a penny is 2/10." This choice corresponds to the actual relative frequency probability calculated earlier. So this answer is correct.
b. "That it is more probable to get tails than it is heads when tossing a penny." This answer could be misleading. Although, in John's specific experiment, he obtained more tails than heads, it does not necessarily mean that tails are more probable in the long run. The relative frequency probability for heads (1/5) is still quite substantial, indicating that heads are not significantly less likely than tails.
c. "That in the long term, the expected relative frequency would be 5/10. Because he has only tossed the penny 10 times, a different pattern has emerged." This answer is incorrect. The expected relative frequency probability for heads in the long term, when a fair coin is used, is 1/2, not 5/10. Although John's experiment yielded different results than what would be expected, it does not provide evidence against the expected long-term relative frequency probability.
In conclusion, John should conclude that the expected relative frequency probability of getting heads when tossing a penny is 2/10 (or 1/5), as stated in option (a).