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

Classification	Frequency
igneous	$10$ $10$
metamorphic	$33$ $33$
sedimentary	$27$ $27$

Each rock in a collection of $70$ rocks was classified as either igneous, metamorphic, or sedimentary, as shown in the frequency table.

If one of these rocks is selected at random, what is the probability of selecting a rock that is igneous?

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Explanation

Choice D is correct. If one of the rocks in the collection is selected at random, the probability of selecting a rock that is igneous is equal to the number of igneous rocks in the collection divided by the total number of rocks in the collection. According to the table, there are $10$ igneous rocks in the collection, and it's given that there's a total of $70$ rocks in the collection. Therefore, if one of the rocks in the collection is selected at random, the probability of selecting a rock that is igneous is $StartFraction 10 Over 70 EndFraction$ .

Choice A is incorrect. This is the number of igneous rocks in the collection divided by the number of sedimentary rocks in the collection, not divided by the total number of rocks in the collection.

Choice B is incorrect. This is the number of igneous rocks in the collection divided by the number of metamorphic rocks in the collection, not divided by the total number of rocks in the collection.

Choice C is incorrect. This is the number of igneous rocks in the collection divided by the number of rocks in the collection that aren't igneous, not divided by the total number of rocks in the collection.