Use table to answer the question.
Plant Types A B C D E
Number of Seedlings 100 140 80 60 40
A former conducted an inventory on his two square kilometers of rainforest; the results are in the table. He plans on randomly selecting a seedling to experiment on when he goes back to the forest. What is the probability that he will randomly pick a type B plant? Write your answer in the simplest form of a fraction.
The total number of seedlings that can be selected from is 100 + 140 + 80 + 60 + 40 = 420.
The number of Type B seedlings is 140.
Probability of selecting a Type B plant = Number of Type B seedlings / Total number of seedlings
Probability of selecting a Type B plant = 140 / 420 = 1/3
Therefore, the probability that the former will randomly pick a Type B plant is 1/3.
The number of bulbs that burnt for more than 1,500 hours out of the 2,500 tested is 2,200.
Probability of a bulb burning for more than 1,500 hours = Number of bulbs burning for more than 1,500 hours / Total number of bulbs tested
Probability = 2,200 / 2,500 = 0.88
Therefore, the likelihood that Lucy's purchased light bulb from Company X will burn for more than 1,500 hours is 0.88.
The total frequency of all outcomes is 20 + 25 + 30 + 10 + 15 = 100.
The frequency of picking the letter R is 30.
Probability of picking the letter R = Frequency of picking R / Total frequency
Probability of picking R = 30 / 100 = 0.30
Converting the probability to a percentage:
Probability in percentage form = 0.30 * 100 = 30%
Therefore, based on the observed frequency, the probability that Jorelle will pick the letter R is 30%.
Let's calculate the expected and experimental probabilities for each outcome based on the frequency provided in the table:
The total frequency is 10 + 9 + 6 + 15 + 13 + 8 = 61.
The expected probability for each outcome is 1/6 since there are 6 faces on the cube.
Expected Probability = 1/6 = 0.1667
The experimental probability for each outcome is calculated as:
Experimental Probability = Frequency of Outcome / Total Frequency
| Outcome | Frequency | Experimental Probability | Absolute Difference |
|---------|-----------|---------------------------|----------------------|
| 2 | 10 | 10/61 ≈ 0.1639 | |0.1639 - 0.1667| ≈ 0.0028 |
| 4 | 9 | 9/61 ≈ 0.1475 | |0.1475 - 0.1667| ≈ 0.0192 |
| 6 | 6 | 6/61 ≈ 0.0984 | |0.0984 - 0.1667| ≈ 0.0683 |
| 8 | 15 | 15/61 ≈ 0.2459 | |0.2459 - 0.1667| ≈ 0.0792 |
| 10 | 13 | 13/61 ≈ 0.2131 | |0.2131 - 0.1667| ≈ 0.0464 |
| 12 | 8 | 8/61 ≈ 0.1311 | |0.1311 - 0.1667| ≈ 0.0356 |
The largest discrepancy between the experimental and expected probability is 0.0792 or 7.92% (rounding to the nearest whole number).
Therefore, the largest discrepancy between the experimental and expected probability of this experiment is 8%.
Company X tested its light bulbs to see how long they would last. On a production line 2,500 bulbs were taken and tested. The department in charge reported that out of 2,500 bulbs, there were 2,200 bulbs that burnt out after more than 1,500 hours of use. Lucy purchased a light bulb from Company X. What is the likelihood that it will burn for more than 1,500 hours? Write your answer in decimal form.
The letter tiles C, A, R, E, and S are placed in a box. Without looking, Jorelle picks a letter tile from the box and records are the result before placing it back. He repeats the procedure 100 times and observes the following results:
Outcomes C A R E S
Frequency 20 25 30 10 15
Based on the observed frequency, what is the probability that Jorelle will pick a letter R? The answer should be in percent form.
Use table to answer the question.
Outcomes 2 4 6 8 10 12
Frequency 10 9 6 15 13 8
Jede tossed a cube with faces numbered with 2, 4, 6, 8, 10,and 12. The results are recorded in the table. What is the largest discrepancy between the experimental and expected probability of this experiment? The answer needs to be in percent from the nearest whole number.
To find the largest discrepancy between the experimental and expected probability, we need to calculate the probability for each outcome based on the experimental frequency and the expected probability.
The total frequency is 10 + 9 + 6 + 15 + 13 + 8 = 61.
The total expected frequency for a fair die with faces numbered 2, 4, 6, 8, 10, and 12 is 1/6 for each number.
Expected frequency for each outcome = Total frequency / 6 = 61 / 6 = 10.1667 (rounded to 4 decimal places).
Now, we can calculate the experimental and expected probabilities for each outcome and find the largest discrepancy.
| Outcome | Frequency | Experimental Probability | Expected Probability |
|---------|-----------|---------------------------|----------------------|
| 2 | 10 | 10/61 ≈ 0.1639 | 1/6 = 0.1667 |
| 4 | 9 | 9/61 ≈ 0.1475 | 1/6 = 0.1667 |
| 6 | 6 | 6/61 ≈ 0.0984 | 1/6 = 0.1667 |
| 8 | 15 | 15/61 ≈ 0.2459 | 1/6 = 0.1667 |
| 10 | 13 | 13/61 ≈ 0.2131 | 1/6 = 0.1667 |
| 12 | 8 | 8/61 ≈ 0.1311 | 1/6 = 0.1667 |
The largest discrepancy between the experimental and expected probability is found by taking the absolute difference between the two probabilities for each outcome and finding the maximum difference.
| Outcome | Absolute Difference |
|---------|----------------------|
| 2 | |0.1667 - 0.1639| ≈ 0.0028 |
| 4 | |0.1667 - 0.1475| ≈ 0.0192 |
| 6 | |0.1667 - 0.0984| ≈ 0.0683 |
| 8 | |0.1667 - 0.2459| ≈ 0.0792 |
| 10 | |0.1667 - 0.2131| ≈ 0.0464 |
| 12 | |0.1667 - 0.1311| ≈ 0.0356 |
The largest discrepancy is 0.0792, or approximately 7.92%.
incorrect
Let's calculate the largest discrepancy between the experimental and expected probability again:
The total frequency is 10 + 9 + 6 + 15 + 13 + 8 = 61.
The expected probability for each outcome is 1/6 since a fair die has 6 faces.
Expected probability = 1/6 ≈ 0.1667
Now, let's calculate the experimental probability for each outcome based on the frequency:
Experimental probability = Frequency of outcome / Total frequency
| Outcome | Frequency | Experimental Probability | Absolute Difference (Experimental - Expected) |
|---------|-----------|---------------------------|-----------------------------------------------|
| 2 | 10 | 10/61 ≈ 0.1639 | |0.1639 - 0.1667| ≈ 0.0028 |
| 4 | 9 | 9/61 ≈ 0.1475 | |0.1475 - 0.1667| ≈ 0.0192 |
| 6 | 6 | 6/61 ≈ 0.0984 | |0.0984 - 0.1667| ≈ 0.0683 |
| 8 | 15 | 15/61 ≈ 0.2459 | |0.2459 - 0.1667| ≈ 0.0792 |
| 10 | 13 | 13/61 ≈ 0.2131 | |0.2131 - 0.1667| ≈ 0.0464 |
| 12 | 8 | 8/61 ≈ 0.1311 | |0.1311 - 0.1667| ≈ 0.0356 |
The largest discrepancy between the experimental and expected probability is 0.0792, or approximately 7.92%. Thank you for your patience.