The table below shows the results of flipping two coins. how does the experimental probability of getting at least one tails compare to the theoretical probability of getting at least one tails
Outcome: HH HT TH TT
# of times Tossed: 28 22 34 16
Question Answers:
A. The experimental probability is 3% greater than the theoretical probability.
B. The theoretical probability is 3% greater than the experimental probability.
C. The experimental probability is equal to the theoretical probability.
D. The experimental probability is about 1% less than the theoretical probability.
theoretically, P(at least 1 tail) = 1 - P(two heads) = 3/4 = 75/100
experimentally, it was 72/100
Are theoretic and experimental rpobablity the same number bot?
Theoretical probability and experimental probability are not always the same. Theoretical probability is what we expect to happen in an ideal situation, while experimental probability is what actually happens when we conduct an experiment. The two can sometimes be very close, especially if the sample size is large, but they can also be quite different due to random chance or other factors.
To determine the experimental probability and theoretical probability of getting at least one tails, we need to calculate the total number of successful outcomes (tail) and the total number of possible outcomes.
Let's start with the experimental probability:
In the given table, there are four possible outcomes: HH, HT, TH, and TT. Out of these outcomes, there are three outcomes with at least one tails: HT, TH, TT. We can add the number of times these outcomes occur to find the total number of successful outcomes: 22 + 34 + 16 = 72.
Similarly, we can find the total number of times the coins were tossed, which is the sum of the number of times each outcome occurred: 28 + 22 + 34 + 16 = 100.
Therefore, the experimental probability of getting at least one tails is 72/100 = 0.72.
Now, let's calculate the theoretical probability:
For each coin flip, there are two possible outcomes, heads (H) or tails (T). The probability of getting tails on one flip is 1/2 or 0.5.
To find the probability of getting at least one tails, we use the complement rule: 1 - probability of getting no tails.
The probability of getting no tails on one flip is 1 - 0.5 = 0.5.
Since we are flipping two coins, we multiply the probability of getting no tails by itself: 0.5 * 0.5 = 0.25.
Therefore, the theoretical probability of getting at least one tails is 1 - 0.25 = 0.75.
Comparing the experimental probability of 0.72 with the theoretical probability of 0.75, we can conclude that the experimental probability is about 1% less than the theoretical probability. So, the answer is option D: The experimental probability is about 1% less than the theoretical probability.