PSAT Math Multiple-Choice Question 403: Answer and Explanation

Question: 403

Table 1

Age of Orange Trees	Percent Distribution
Less than 3 years old	15%
3–5 years old	20%
6–10 years old	25%
Older than 10 years	40%

A large fruit orchard has 2,500 orange trees. Table 1 above shows the distribution of ages of the orange trees in the orchard. A county inspector has been notified that a highly contagious bacterial disease called citrus canker has infected some of the orange trees. The inspector randomly tests 4% of each age group of the trees. Her findings are shown in Table 2 below.

Table 2

Age of Orange Trees	Number with Citrus Cankers
Less than 3 years old	8
3–5 years old	6
6–10 years old	8
Older than 10 years	3

What is the probability that an orange tree selected at random from the tested trees less than 3 years old will have citrus canker?

• A. 0.03
• B. 0.12
• C. 0.15
• D. 0.53

Correct Answer: D

Explanation:

D

Difficulty: Hard

Getting to the Answer: The probability that one tree less than 3 years old randomly selected from those that were tested would have cankers is equal to the number of trees less than 3 years old that had cankers divided by the total number of trees less than 3 years old that were tested. This means you need only two numbers to answer the question. One of those numbers is in the second table—8 trees less than 3 years old had cankers. Finding the other number is the tricky part. Use information from the -question stem and Table 1. The inspector tested 4% of the total number of trees less than 3 years old, or 4% of 15% of 2,500 trees. Multiply to find that 0.04 × 0.15 × 2,500 = 15 trees less than 3 years old were tested. This means the probability is , which matches choice (D).