An agricultural researcher categorized a sample of 150 tomato plants by their watering sch… — SAT

An agricultural researcher categorized a sample of $150$ 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	$62$	$18$	$80$
Weekly	$28$	$42$	$70$
Total	$90$	$60$	$150$

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
$\frac{14}{75}$
B
$\frac{2}{5}$
$\frac{14}{45}$ Cevap
D
$\frac{31}{45}$

Cevap

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.

Adım Adım Çözüm

Identify the condition specified in the question stem to determine the subset of data to consider.

The condition is 'given that a tomato plant ... produced a high yield of fruit'. Thus, we restrict our focus to the 'High Yield' column.

This establishes the denominator for the conditional probability calculation.

Find the total number of plants in the 'High Yield' column (denominator) and the number of those plants that had a weekly watering schedule (numerator).

Total high-yield plants = 90. High-yield plants with a weekly watering schedule = 28.

These represent the total possible outcomes and the favorable outcomes within the restricted sample space.

Calculate and simplify the fraction representing the conditional probability.

Probability = \frac{28}{90} = \frac{14}{45}.

Expressing the final ratio in its simplest fractional form to match the standard exam options.

Anahtar Kavram

Two-Way Tables and Conditional Probability

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