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Probability and conditional probability SAT question

Math · Problem-Solving and Data Analysis · Easy · Answer it here, explanation included.

The table gives the distribution of votes for a new school mascot and grade level for $80$ students.

Mascot	Grade level
Mascot	Sixth	Seventh	Eighth	Total
Badger	$4$	$9$	$9$	$22$
Lion	$9$	$2$	$9$	$20$
Longhorn	$4$	$6$	$4$	$14$
Tiger	$6$	$9$	$9$	$24$
Total	$23$	$26$	$31$	$80$

If one of these students is selected at random, what is the probability of selecting a student whose vote for new mascot was for a lion?

ExplanationShow

Choice C is correct. If one of these students is selected at random, the probability of selecting a student whose vote for the new mascot was for a lion is given by the number of votes for a lion divided by the total number of votes. The given table indicates that the number of votes for a lion is $20$ votes, and the total number of votes is $80$ votes. The table gives the distribution of votes for $80$ students, and the table shows a total of 80 votes were counted. It follows that each of the $80$ students voted exactly once. Thus, the probability of selecting a student whose vote for the new mascot was for a lion is $\frac{20}{80}$ , or $\frac{1}{4}$ .

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

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

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

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