Question

question 2 of 5
select the correct answer.
the results from a test to detect the presence of a nutrient in a soil sample are shown in the table.

	test is positive	test is negative	total
doesnt contain nutrient	18	282	300
total	493	307	800

what is the probability that the result of the test is negative, given that the sample doesnt contain the nutrient?

• 96%
• 92%
• 95%
• 94%

Explanation:

Step1: Identify the relevant values

We need the number of samples that don't contain the nutrient and test negative, and the total number of samples that don't contain the nutrient. From the table, the number of samples that don't contain the nutrient and test negative is 282, and the total number of samples that don't contain the nutrient is 300.

Step2: Calculate the probability

The probability is the number of favorable outcomes (test negative and no nutrient) divided by the number of possible outcomes (no nutrient). So we calculate $\frac{282}{300}$.

Step3: Convert to percentage

To convert to a percentage, multiply by 100: $\frac{282}{300} \times 100 = 94\%$? Wait, no, wait: 282 divided by 300 is 0.94? Wait, 282 ÷ 300 = 0.94? Wait, 300 × 0.94 = 282? Wait, 300 × 0.96 = 288. Wait, I made a mistake. Let's recalculate: 282 ÷ 300. Let's divide numerator and denominator by 6: 282 ÷ 6 = 47, 300 ÷ 6 = 50. 47/50 = 0.94? Wait, no, 47×2=94, 50×2=100. So 47/50 = 94/100 = 0.94, which is 94%? Wait, but wait, the table: "Doesn't contain nutrient" row: test positive is 18, test negative is 282, total 300. So the number of negative tests given no nutrient is 282, total no nutrient is 300. So 282/300 = 0.94, which is 94%? Wait, but let's check again. 282 divided by 300: 300 goes into 282 zero times. 300 goes into 2820 nine times (9×300=2700), remainder 120. 300 goes into 1200 four times (4×300=1200). So 0.94, which is 94%. Wait, but the options have 96%, 92%, 95%, 94%. So 282/300 = 0.94 = 94%? Wait, no, 282 ÷ 300: let's simplify the fraction. Divide numerator and denominator by 6: 282 ÷ 6 = 47, 300 ÷ 6 = 50. 47/50 = 0.94, so 94%. Wait, but wait, maybe I misread the table. Let me check again: "Doesn't contain nutrient" row: test positive 18, test negative 282, total 300. So yes, 282 out of 300. So 282/300 = 0.94, which is 94%? Wait, but 282 divided by 300: 300 × 0.96 = 288, which is more than 282. 300 × 0.94 = 282. Yes, so 282/300 = 0.94 = 94%. Wait, but the first option is 96%. Wait, maybe I mixed up the rows. Wait, "Contains nutrient" row: test negative is 25, total 500. "Doesn't contain" row: test negative is 282, total 300. So the question is: probability that test is negative given that sample doesn't contain nutrient. So it's P(negative | no nutrient) = P(negative and no nutrient) / P(no nutrient) = 282/300 = 0.94 = 94%. So the answer is 94%.

Answer:

94% (the option with 94%)