In which scenario is the experimental probability equal to the theoretical probability?(1 point)
Responses
A coin is flipped six times and the head appears each time.
A coin is flipped six times and the head appears each time.
A coin is flipped six times and the head appears five times.
A coin is flipped six times and the head appears five times.
A coin is flipped six times and the head appears three times.
A coin is flipped six times and the head appears three times.
A coin is flipped six times and the head appears four times.
In order to determine the scenario where the experimental probability is equal to the theoretical probability, we need to understand what experimental and theoretical probabilities are.
Experimental probability is the probability that an event will occur based on the results of an actual experiment or observation. It is determined by conducting trials or experiments and counting the number of times the event occurs relative to the total number of trials.
Theoretical probability, on the other hand, is the probability of an event occurring based on mathematical calculations or theoretical calculations. It is determined by considering all the possible outcomes and assigning probabilities based on mathematical principles.
In this case, the question asks for the scenario where the experimental probability is equal to the theoretical probability. To find the theoretical probability, we need to calculate the probability of getting heads in a coin flip.
Since a coin has two sides (heads and tails) and is a fair coin, the probability of getting heads on any particular flip is 1/2 or 0.5.
Now let's analyze the given scenarios:
1. A coin is flipped six times and the head appears each time.
In this scenario, the experimental probability of getting heads is 6/6, which simplifies to 1. This means that heads occurs on every flip. The theoretical probability is also 0.5. Therefore, the experimental and theoretical probabilities are not equal.
2. A coin is flipped six times and the head appears five times.
In this scenario, the experimental probability of getting heads is 5/6 or approximately 0.833. The theoretical probability is still 0.5. Therefore, the experimental and theoretical probabilities are not equal.
3. A coin is flipped six times and the head appears three times.
In this scenario, the experimental probability of getting heads is 3/6, which simplifies to 0.5. The theoretical probability is also 0.5. Therefore, the experimental and theoretical probabilities are equal.
4. A coin is flipped six times and the head appears four times.
In this scenario, the experimental probability of getting heads is 4/6 or approximately 0.667. The theoretical probability is still 0.5. Therefore, the experimental and theoretical probabilities are not equal.
Based on the analysis, the only scenario where the experimental probability is equal to the theoretical probability is when the coin is flipped six times and the head appears three times.
A coin is flipped six times and the head appears three times. (Experimental probability and theoretical probability are the same when all possible outcomes are equally likely and the sample size is large enough for the law of large numbers to apply.)
A coin is flipped 150 times. The results of the experiment are shown in the following table:
Heads Tails
63 87
Which of the following statements best describes the experimental probability of getting heads? (5 points)
It is equal to the theoretical probability.
It is 8% lower than the theoretical probability.
It is 8% higher than the theoretical probability.
The experimental probability cannot be concluded from the data in the table.
The experimental probability of getting heads can be calculated by dividing the number of heads by the total number of flips: 63/150 = 0.42 or 42%.
Since the theoretical probability of getting heads on a fair coin is 0.5 or 50%, we can compare the experimental and theoretical probabilities to determine the difference.
The experimental probability of getting heads is 8% lower than the theoretical probability.
Therefore, the correct answer is: It is 8% lower than the theoretical probability.