A forester classified 250 trees in a park by species and... | SAT Probability and conditional probability Question, Answer Explained

Question bank / Probability and conditional probability

Math · Problem-Solving and Data AnalysisMedium

Species	Healthy	Diseased	Total
Oak	92	18	110
Maple	68	12	80
Pine	40	20	60
Total	200	50	250

A forester classified $250$ trees in a park by species and health, as shown in the table. If one of the diseased trees is selected at random, what is the probability that it is an oak?

$\frac{9}{125}$

$\frac{9}{55}$

$\frac{9}{25}$

$\frac{11}{25}$

Show answer and explanation

Answer: C

Only the $50$ diseased trees can be selected, and $18$ of them are oaks. So the probability is $\frac{18}{50} = \frac{9}{25}$ .

Choice B is $\frac{18}{110}$ , the probability that an oak is diseased, but here the selected tree is known to be diseased, so the denominator is $50$ .

Why the other choices are wrong

A. This divides 18 by all 250 trees, but the tree is selected only from the 50 diseased trees.
B. This is 18 out of 110, the probability that an oak is diseased, which reverses the condition.
D. 11/25 is 110 out of 250, the probability that any tree is an oak.

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