An agricultural researcher categorized a sample of tomato plants by their watering schedule (daily or weekly) and their fruit yield (high yield or average yield). The results are summarized in the table below.
| Watering Schedule | High Yield | Average Yield | Total |
|---|---|---|---|
| Daily | |||
| Weekly | |||
| Total |
Given that a tomato plant selected at random from the sample produced a high yield of fruit, what is the probability that the plant had a weekly watering schedule?
- A
- B
- Answer
- D
Answer
The correct answer is fourteen-forty-fifths (14/45). Given that the plant has a high yield, the sample space is restricted to the 90 plants in the High Yield column. Out of these 90 plants, 28 were on a weekly watering schedule, resulting in a probability of 28/90, which simplifies to 14/45.
To find the conditional probability that a tomato plant had a weekly watering schedule given that it produced a high yield of fruit, restrict the denominator to the total number of high-yield plants, which is 90. The numerator is the number of plants that meet both conditions (weekly watering and high yield), which is 28. The probability is 28/90, which simplifies to 14/45.
Step-by-Step Solution
Key Concept
Two-Way Tables and Conditional Probability
Estimated Time:1m 30s