sat suite question viewer

Problem-Solving and Data Analysis / Probability and conditional probability Difficulty: Hard

A grove has $6$ rows of birch trees and $5$ rows of maple trees. Each row of birch trees has $8$ trees $20$ feet or taller and $6$ trees shorter than $20$ feet. Each row of maple trees has $9$ trees $20$ feet or taller and $7$ trees shorter than $20$ feet. A tree from one of these rows will be selected at random. What is the probability of selecting a maple tree, given that the tree is $20$ feet or taller?

Back question 37 of 46 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Explanation

Choice C is correct. If a tree from one of these rows is selected at random, the probability of selecting a maple tree, given that the tree is $20$ feet or taller, is equal to the number of maple trees that are $20$ feet or taller divided by the total number of trees that are $20$ feet or taller. It's given that there are $6$ rows of birch trees, and each row of birch trees has $8$ trees that are $20$ feet or taller. This means that there are a total of $6 left parenthesis 8 right parenthesis$ , or $48$ , birch trees that are $20$ feet or taller. It's given that there are $5$ rows of maple trees, and each row of maple trees has $9$ trees that are $20$ feet or taller. This means that there are a total of $5 left parenthesis 9 right parenthesis$ , or $45$ , maple trees that are $20$ feet or taller. It follows that there are a total of $48 plus 45$ , or $93$ , trees that are $20$ feet or taller. Therefore, the probability of selecting a maple tree, given that the tree is $20$ feet or taller, is $StartFraction 45 Over 93 EndFraction$ , or $StartFraction 15 Over 31 EndFraction$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.