You toss a coin 50 times and get 12 tails. What is the empirical probability of getting heads? Write your answer in percent form.(1 point) Responses 1925 Start Fraction 19 over 25 End Fraction 0.76 0.76 24% 24% 76%
The empirical probability of getting heads can be calculated by subtracting the number of tails from the total number of tosses, then dividing by the total number of tosses.
Total number of tosses = 50
Number of tails = 12
Number of heads = 50 - 12 = 38
Empirical probability of getting heads = Number of heads / Total number of tosses
Empirical probability of getting heads = 38 / 50
Empirical probability of getting heads = 0.76
In percentage form, 0.76 can be written as 76%.
Therefore, the empirical probability of getting heads is 76%.
4. 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 four times. A coin is flipped six times and the head appears four times. 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 each time.
Theoretical probability is based on mathematical calculations and does not involve any physical experiment, whereas experimental probability is based on the results of actual experiments or trials.
In this case, the theoretical probability of getting heads when flipping a fair coin is 0.5 (50%), as there are only two possible outcomes - heads or tails, and they are equally likely.
Now, let's analyze each scenario:
1. A coin is flipped six times and the head appears four times.
This scenario is an experimental probability, which may or may not be equal to the theoretical probability of 0.5.
2. A coin is flipped six times and the head appears five times.
This scenario is an experimental probability, which may or may not be equal to the theoretical probability of 0.5.
3. A coin is flipped six times and the head appears three times.
This scenario is an experimental probability, which may or may not be equal to the theoretical probability of 0.5.
4. A coin is flipped six times and the head appears each time.
This scenario has a theoretical probability of 1 (100%) for getting heads each time, which is not the same as the theoretical probability of 0.5.
Therefore, the scenario where the experimental probability is most likely to equal the theoretical probability is:
A coin is flipped six times and the head appears each time.
3. A quality controller inspected 1,000 units of a product and rejected 150 units due to defects. Approximate the empirical probability that a unit will pass the inspection.(1 point) Responses 1.5% 1.5% 0.15% 0.15% 1720 Start Fraction 17 over 20 End Fraction 320
To approximate the empirical probability that a unit will pass the inspection, we need to calculate the number of units that passed the inspection first.
Number of units that passed the inspection = Total units inspected - Number of units rejected
Number of units that passed the inspection = 1000 - 150
Number of units that passed the inspection = 850
Empirical probability of a unit passing the inspection = Number of units that passed the inspection / Total units inspected
Empirical probability of a unit passing the inspection = 850 / 1000
Empirical probability of a unit passing the inspection = 0.85
In percentage form, 0.85 can be written as 85%.
Therefore, the empirical probability that a unit will pass the inspection is 85%.