a quality controller inspected 1,000 units of a product rejected 150 units due to defects. Approximate the empirical probability that a unit will pass the inspection.
a. 1.5%
b. 3/20
c. 0.15%
d. 17/20
Theoretical probability refers to the probability of an event based on the assumption that all outcomes are equally likely. In the case of flipping a fair coin, the theoretical probability of getting heads would be 1/2, as there are two possible outcomes (heads or tails) and they are equally likely.
Experimental probability refers to the probability of an event based on actual experiment or observation.
In this context, the scenario where the experimental probability is equal to the theoretical probability would be when a fair coin is flipped six times and the head appears exactly three times. This is because the theoretical probability of getting heads on any single flip of a fair coin is 1/2, and the experimental probability should ideally approach 1/2 when the number of trials is large.
Therefore, the correct scenario is:
b. A coin is flipped six times and the head appears three times.
Since participants have an equal chance of receiving each type of coupon and there are three types of coupons (skiing, snow tubing, sleigh rides), the probability of receiving a sleigh ride coupon for each participant is 1/3.
To find the expected number of participants who would receive a sleigh ride coupon out of 900 participants, we multiply the total number of participants by the probability of receiving a sleigh ride coupon:
Expected number of participants with a sleigh ride coupon = 900 * 1/3
Expected number of participants with a sleigh ride coupon = 300
Therefore, the expected number of participants who would receive a coupon for sleigh rides out of 900 participants is 300.
The closest answer choice is:
b. 300
The relative frequency is the number of times an event occurs divided by the total number of opportunities for the event to occur. In this case, the event is a non-defective unit, and we need to calculate the relative frequency of a non-defective unit.
Number of non-defective units = Total units - Number of defective units
Number of non-defective units = 500 - 25
Number of non-defective units = 475
Relative frequency of a non-defective unit = Number of non-defective units / Total units
Relative frequency of a non-defective unit = 475 / 500
Relative frequency of a non-defective unit = 19 / 20
Therefore, the relative frequency of a non-defective unit from this batch of items is 19/20.
The answer is:
c. 19/20
To find the empirical probability of getting heads, we first need to calculate the number of heads obtained in the experiment.
Number of heads = Total tosses - Number of tails
Number of heads = 50 - 12
Number of heads = 38
Now, calculate the empirical probability of getting heads:
Empirical probability of getting heads = Number of heads / Total tosses
Empirical probability of getting heads = 38 / 50
Empirical probability of getting heads = 0.76
Convert 0.76 to percentage:
0.76 * 100 = 76%
Therefore, the empirical probability of getting heads is 76%.
The answer is:
b. 76%
all correct answers:
question 1: 19/20
question 2: 76%
question 3: 17/20
question 4: a coin is flipped 3 times and head appears THREE TIMES
question 5: 30
To find the empirical probability that a unit will pass the inspection, we need to calculate the number of units that passed the inspection.
Number of units that passed the inspection = Total units - Number of units rejected
Number of units that passed the inspection = 1000 - 150
Number of units that passed the inspection = 850
Empirical probability that a unit will pass the inspection = Number of units that passed the inspection / Total units
Empirical probability that a unit will pass the inspection = 850 / 1000
Empirical probability that a unit will pass the inspection = 0.85
Convert 0.85 to percentage:
0.85 * 100 = 85%
Therefore, the empirical probability that a unit will pass the inspection is 85%.
None of the provided answer options match this calculation, so the closest option would be:
b. 3/20 (which is equivalent to 15%)
In which scenario is the experimental probability equal to the theoretical probability?
a. A coin is flipped six times and the head appears five times.
b. A coin is flipped six times and the head appears three times.
c. A coin is flipped six times and the head appears four times.
d. A coin is flipped six times and the head appears each times.
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 rides. 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
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. 25/500
b. 1/20
c. 19/20
d. 475/500
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. 19/25
b. 76%
c. 0.76
d. 24%