A farmer conducted an inventory on his two square kilometers of rainforest. he has 100 A seedlings, 140 B seedlings, 80 C seedlings, 60 D seedlings, and 40 E seedlings. 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.
There are a total of 420 seedlings (100+140+80+60+40) in the two square kilometers of rainforest.
The probability of selecting a type B seedling is 140/420, which simplifies to 1/3.
Therefore, the probability of randomly selecting a type B plant is 1/3.
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.
Out of the 2,500 bulbs tested, 2,200 burnt out after more than 1,500 hours of use. Therefore, the proportion of bulbs that lasted more than 1,500 hours is 2,200/2,500 = 0.88.
The probability that Lucy's light bulb from Company X will burn for more than 1,500 hours is also 0.88, assuming that her bulb is from the same production line and has the same quality as the 2,500 bulbs that were tested.
Therefore, the likelihood that Lucy's light bulb from Company X will burn for more than 1,500 hours is 0.88 expressed as a decimal.
Answer: 0.88
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 the result before placing it back. He repeats the procedure 100 times and observes the following results: C was picked 20 times, A was picked 25 times, R was picked 30 times, E was picked 10 times, and S was picked 15 times. Based on the observed frequency, what is the probability that Jorelle will pick a letter R? The answer should be in percent form.
Jorelle picked a letter tile 100 times.
Out of the 100 times, the letter R was picked 30 times.
The probability of picking the letter R in one draw is the frequency of R divided by the total number of draws:
30/100 = 0.3
To convert to percentage form, we can multiply by 100:
0.3 x 100 = 30%
Therefore, the probability that Jorelle will pick the letter R is 30%.
Use the 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 the expected probability of this experiment? The answer needs to be in percent form to the nearest whole number.
There are a total of 10+9+6+15+13+8=61 outcomes in the experiment.
The expected probability of each outcome is 1/6, since there are 6 equally likely outcomes on the cube.
To calculate the experimental probability, we divide the frequency of each outcome by the total number of outcomes (61 in this case).
The table below shows all the probabilities:
Outcome | Frequency | Experimental Probability | Expected Probability | Discrepancy
--- | --- | --- | --- | ---
2 | 10 | 10/61 = 0.164 | 1/6 = 0.167 | 0.003
4 | 9 | 9/61 = 0.148 | 1/6 = 0.167 | 0.019
6 | 6 | 6/61 = 0.098 | 1/6 = 0.167 | 0.069
8 | 15 | 15/61 = 0.246 | 1/6 = 0.167 | 0.079
10 | 13 | 13/61 = 0.213 | 1/6 = 0.167 | 0.046
12 | 8 | 8/61 = 0.131 | 1/6 = 0.167 | 0.036
The largest discrepancy is 0.079 or 7.9%, which occurs for the outcome 8.
Therefore, the largest discrepancy between the experimental and expected probability of this experiment is 7.9%.
Jede tossed a cube with faces numbered with 2, 4, 6, 8, 10, and 12. 2 was landed on 10 times, 4 was landed on 9 times, 6 was landed on 6 times, 8 was landed on 15 times, 10 was landed on 13 times, and 12 was landed on 8 times. What is the largest discrepancy between the experimental and the expected probability of this experiment? The answer needs to be in percent form to the nearest whole number.
There are 6 possible outcomes, each with an expected probability of 1/6 or approximately 16.7%, since there are six equally likely outcomes on the cube.
To calculate the experimental probability of each outcome, we divide the number of times it was landed on by the total number of tosses:
- P(2) = 10/61 = 0.164
- P(4) = 9/61 ≈ 0.148
- P(6) = 6/61 ≈ 0.098
- P(8) = 15/61 ≈ 0.246
- P(10) = 13/61 ≈ 0.213
- P(12) = 8/61 ≈ 0.131
To find the largest discrepancy, we need to find the absolute value of the difference between the experimental and expected probabilities for each outcome, and then find the largest value among those differences:
- |0.164 - 0.167| ≈ 0.003
- |0.148 - 0.167| ≈ 0.019
- |0.098 - 0.167| ≈ 0.069
- |0.246 - 0.167| ≈ 0.079
- |0.213 - 0.167| ≈ 0.046
- |0.131 - 0.167| ≈ 0.036
The largest discrepancy is approximately 0.079 or 7.9%, which occurs for the outcome 8.
Therefore, the largest discrepancy between the experimental and expected probability of this experiment is 7.9% to the nearest whole number.
To find the probability of randomly picking a type B seedling, we need to know the total number of seedlings available. In this case, the farmer has 100 A seedlings, 140 B seedlings, 80 C seedlings, 60 D seedlings, and 40 E seedlings.
The total number of seedlings is given by adding up the number of each type of seedling:
Total number of seedlings = 100 (A) + 140 (B) + 80 (C) + 60 (D) + 40 (E) = 420
Now, we can calculate the probability of picking a type B seedling by dividing the number of B seedlings by the total number of seedlings:
Probability of picking a type B seedling = Number of B seedlings / Total number of seedlings
Probability of picking a type B seedling = 140 / 420
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 140.
Probability of picking a type B seedling = (140 ÷ 140) / (420 ÷ 140)
Probability of picking a type B seedling = 1 / 3
Therefore, the probability that the farmer will randomly pick a type B plant is 1/3.