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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #51 : Probability

In a hotel with 120 rooms, 30 of them have red carpet. A hotel manager has lost his keys somewhere in the hotel. If there is an equal chance of the keys being in any room, what is the probability that they are in a room with red carpet?

Possible Answers:

$\small \frac{1}{3}$

$\small \frac{1}{6}$

$\small \frac{1}{5}$

$\small \frac{1}{4}$

$\small \frac{1}{2}$

Correct answer:

$\small \frac{1}{4}$

Explanation:

Probability = desired outcomes divided by total possible outcomes

$\small \frac{30}{120}=\frac{1}{4}$

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Example Question #61 : How To Find The Probability Of An Outcome

A bag contains the following numbers of apples: 12 red delicious, 10 granny smith, and 7 fuji apples. If an apple is selected at random, what is the probability it is either a granny smith or a fuji apple?

Possible Answers:

$\small \frac{3}{29}$

$\small \frac{12}{29}$

$\small \frac{19}{29}$

$\small \frac{7}{29}$

$\small \frac{17}{29}$

Correct answer:

$\small \frac{17}{29}$

Explanation:

Probability = desired outcomes divided by total possible outcomes. Desired outcome can be either fuji or granny smith.

Desired outcomes =7+10=17

Total outcomes =12+10+7=29

$\small \frac{17}{29}$

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Example Question #58 : Probability

From a class consisting of 15 girls and 12 boys, two students are chosen at random to be class representatives. What is the probability that neither of the two students chosen is a boy?

Possible Answers:

$\small \frac{16}{81}$

$\small \frac{44}{234}$

$\small \frac{25}{81}$

$\small \frac{35}{117}$

$\small \frac{44}{117}$

Correct answer:

$\small \frac{35}{117}$

Explanation:

To satisfy the question, BOTH students chosen must be girls.

First selection: 15 girls of 27 total students:

$\small \small \frac{15}{27}=\frac{5}{9}$

Second selection: 14 girls out of 26 total students:

$\small \frac{14}{26}=\frac{7}{13}$

$\small \frac{5}{9}\times\frac{7}{13}=\frac{35}{117}$

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Example Question #59 : Probability

If 2 six-sided dice, each with sides numbered 1-6, are rolled, what is the probability that the sum of the numbers on the face-up sides is equal to 7?

Possible Answers:

$\small \frac{1}{3}$

$\small \frac{5}{36}$

$\small \frac{1}{4}$

$\small \frac{1}{12}$

$\small \frac{1}{6}$

Correct answer:

$\small \frac{1}{6}$

Explanation:

Probability = desired outcomes divided by total possible outcomes.

Desired outcomes = 6 (1,6; 2,5; 3,4; 4,3; 5,2; 6;1)

Total outcomes - 36 $\left ( 6\times 6 \right )$

$\small \frac{6}{36}\:=\:\frac{1}{6}$

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Example Question #61 : How To Find The Probability Of An Outcome

If an 8-sided die is rolled 3 times, what is the probability that the same number will be rolled each time?

Possible Answers:

$\small \frac{1}{256}$

$\small \frac{1}{512}$

$\small \frac{1}{16}$

$\small \frac{1}{24}$

$\small \frac{1}{64}$

Correct answer:

$\small \frac{1}{64}$

Explanation:

$\small \textup{The first roll can be any number, so we only need be concerned with the}$

$\small \textup{2nd and 3rd rolls, each of which have a}\,\frac{1}{8}\,\textup{chance of being the same as the first}$

$\small \frac{1}{8}\times\frac{1}{8}=\frac{1}{64}$

Another way to look a it is there are 512 total possible outcomes $\left ( 8\times 8\times 8 \right )$ and 8 desired outcomes.

$\small \frac{8}{512}=\frac{1}{64}$

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Example Question #61 : How To Find The Probability Of An Outcome

If a two-sided coin is flipped four times, what is the probability of never getting a head?

Possible Answers:

$\frac{1}{16}$

$\frac{5}{16}$

$\frac{7}{16}$

$\frac{1}{2}$

$\frac{3}{8}$

Correct answer:

$\frac{1}{16}$

Explanation:

The probability of never getting a head is the same as always getting tails. This is $\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{16}$ .

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Example Question #61 : How To Find The Probability Of An Outcome

If a six-sided die is thrown four times, what is the probability of getting a four everytime?

Possible Answers:

$\frac{1}{50}$

$\frac{1}{1296}$

$\frac{1}{7776}$

$\frac{1}{2}$

$\frac{1}{216}$

Correct answer:

$\frac{1}{1296}$

Explanation:

The probability is $\frac{1}{6}\times \frac{1}{6}\times \frac{1}{6}\times \frac{1}{6}=\frac{1}{1296}$ .

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Example Question #222 : Data Analysis

If there are 9 marbles in a bag, three white, three blue, and three red, what is the probability of selecting three red marbles at random?

Possible Answers:

$\frac{1}{80}$

$\frac{1}{64}$

$\frac{1}{85}$

$\frac{1}{90}$

$\frac{1}{84}$

Correct answer:

$\frac{1}{84}$

Explanation:

The probability of selecting 3 red marbles is $\frac{3}{9}\times \frac{2}{8}\times \frac{1}{7}=\frac{1}{84}$ .

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Example Question #61 : How To Find The Probability Of An Outcome

There is a box containing 2 red marbles, 7 blue marbles, and an unknown number of green marbles. If the probably of drawing a red marble is 10%, what is the probably that one draws a green marble?

Possible Answers:

$55\%$

$20\%$

$70\%$

$50\%$

$60\%$

Correct answer:

$55\%$

Explanation:

Let $x$ be the total number of marbles in the box. Since there's a 10% chance of drawing a red marble, then $0.1x=2$ implies there are 20 marbles total in the box. Thus, there are only 11 green marbles, resulting in the probability of drawing a green marble being $\frac{11}{20}=55\%$

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Example Question #222 : Data Analysis

A person rolls a fair 6-sided die twice. What is the probability that the sum of the two rolls is 3?

Possible Answers:

$\frac{1}{18}$

$\frac{2}{9}$

$\frac{1}{3}$

$\frac{1}{36}$

$\frac{1}{9}$

Correct answer:

$\frac{1}{18}$

Explanation:

In order for the sum to be 3, the two rolls must be 1 and 2. However, it doesn't matter which one comes first. Therefore, there are 2 ways we can acquire the sum being 3. The total number of combination of two die is $6\cdot 6=36$ .

Thus, the probability of rolling a sum of 3 is $\frac{2}{36}=\frac{1}{18}$ .

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #51 : Probability

Example Question #61 : How To Find The Probability Of An Outcome

Example Question #58 : Probability

Example Question #59 : Probability

Example Question #61 : How To Find The Probability Of An Outcome

Example Question #61 : How To Find The Probability Of An Outcome

Example Question #61 : How To Find The Probability Of An Outcome

Example Question #222 : Data Analysis

Example Question #61 : How To Find The Probability Of An Outcome

Example Question #222 : Data Analysis

All SAT Math Resources

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