A calculator manufacturing company checks 500 calculator units, and 25 of them have non-functioning keys. Approximate the relative frequency of a non-defective unit from this batch of items. Express your answer in the simplest form of a fraction.
A. 475/500
B. 25/500
C. 19/20
D. 1/20
ANSWERS TO UNIT 8 LESSON 3 QUICK CHECK
1. 19/20
2. 76%
3. 17/20
4. A coin is flipped six times and the head appears three times.
5. 300
You toss a coin 50 times and get 12 tails. What is the empirical probability of getting heads? Write your answer in percent form.
A. 24%
B. 0.76
C. 76%
D. 19/25
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.
A. 3/20
B. 0.15%
C. 17/20
D. 1.5%
In which scenario is the experimental probability equal to the theoretical probability?
A. A coin is flipped six times and the head appears each time.
B. A coin is flipped six times and the head appears four times.
C. A coin is flipped six times and the head appears five times.
D. A coin is flipped six times and the head appears three times.
Theoretical probability is the probability based on mathematical reasoning and can be calculated by finding the ratio of the number of favorable outcomes to the total number of outcomes.
Experimental probability is the probability observed in an experiment or simulation.
In the case of flipping a fair coin, the theoretical probability of getting a head on any single flip is 0.5.
A. If a coin is flipped six times and the head appears each time, this scenario is less likely because the probability of getting a head on each flip is 0.5, and the probability of getting a head on all six flips consecutively is (0.5)^6 = 1/64. This is not a common occurrence.
B. If a coin is flipped six times and the head appears four times, the experimental probability of getting a head is different from the theoretical probability.
C. If a coin is flipped six times and the head appears five times, this scenario is less likely because the probability of getting a head on each flip is 0.5, and the probability of getting a head five times out of six flips is calculated as 6C5 * (0.5)^5 * (0.5)^1 = 6/64.
D. If a coin is flipped six times and the head appears three times, the experimental probability could be closer to the theoretical probability of 0.5 on each flip.
Based on the options provided, option D is the most likely scenario where the experimental probability is equal to the theoretical probability.
As part of a promotion, people who participate in a survey are sent a free coupon for one of three winter activities: Skiing, Snow tubing, or Sleigh rids. Participants have an equal chance of receiving each type of coupon. If 900 people participate, how many would be expected to receive a coupon for sleigh rides?
A. 450
B. 300
C. 600
D. 2/3
Since each participant has an equal chance of receiving each type of coupon and there are three options, the probability of receiving a coupon for sleigh rides is 1/3.
To find the expected number of people who would receive a coupon for sleigh rides, we multiply the total number of participants by the probability of receiving a coupon for sleigh rides:
Expected number of people receiving a coupon for sleigh rides = Total number of participants * Probability of receiving a coupon for sleigh rides
Expected number of people receiving a coupon for sleigh rides = 900 * 1/3
Expected number of people receiving a coupon for sleigh rides = 300
Therefore, it is expected that 300 people would receive a coupon for sleigh rides. The answer is B. 300.
Great! If you have any more questions or need further assistance, feel free to ask.
A. 475/500
To find the relative frequency of a non-defective unit, we need to subtract the number of defective units from the total number of units and then divide by the total number of units.
Relative frequency of non-defective units = (Total units - Defective units) / Total units
= (500 - 25) / 500
= 475 / 500
Therefore, the relative frequency of a non-defective unit from this batch of items is 475/500.
To find the empirical probability of getting heads, we can use the formula:
Empirical Probability = Number of times the event occurs / Total number of trials
In this case, the total number of trials is 50 and the number of tails is 12. Since there are only two outcomes (heads or tails) when tossing a coin:
Number of heads = Total number of trials - Number of tails
Number of heads = 50 - 12
Number of heads = 38
Empirical Probability of getting heads = Number of heads / Total number of trials
Empirical Probability of getting heads = 38 / 50
Empirical Probability of getting heads = 0.76
Converting 0.76 to percentage form gives us 76%.
Therefore, the empirical probability of getting heads is 76%. The correct answer is C. 76%.