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PSAT Math : PSAT Mathematics

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Example Questions

Example Question #62 : 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:

$\frac{1}{1296}$

$\frac{1}{2}$

$\frac{1}{216}$

$\frac{1}{50}$

$\frac{1}{7776}$

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 #62 : Probability

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:

$\frac{1}{90}$

$\frac{1}{84}$

$\frac{1}{64}$

$\frac{1}{80}$

$\frac{1}{85}$

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 #1511 : Psat Mathematics

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:

$55\%$

$20\%$

$60\%$

$70\%$

$50\%$

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 #63 : How To Find The Probability Of An Outcome

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

Possible Answers:

$\frac{1}{36}$

$\frac{1}{18}$

$\frac{1}{9}$

$\frac{2}{9}$

$\frac{1}{3}$

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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Example Question #66 : How To Find The Probability Of An Outcome

A card is drawn randomly from a stardard 52-card deck. What is the probability of drawing a four of hearts?

Possible Answers:

$\frac{3}{52}$

$\frac{1}{13}$

$\frac{1}{4}$

$\frac{1}{52}$

$\frac{2}{13}$

Correct answer:

$\frac{1}{52}$

Explanation:

The question is asking for the probability of drawing a 4 AND a Heart.

Prob(draw a 4) $=\frac{4}{52}=\frac{1}{13}$ .

Prob(draw a Heart) $=\frac{13}{52}=\frac{1}{4}$ .

Then the Prob(4 AND Heart) = Prob(4) * Prob(Heart) $=\frac{1}{13}\cdot \frac{1}{4}=\frac{1}{52}$

You can also solve this question using logic instead of the rules of probability. We know there is only one four of hearts in a deck of cards, so the probability of drawing one must be $\frac{1}{52}$ .

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Example Question #1512 : Psat Mathematics

How many different ways can 15 runners receive ribbons in a race if 1st, 2nd, 3rd, and 4th place ribbons are given?

Possible Answers:

$_{4}P_{15}$

$15!$

$_{4}C_{15}$

$_{15}P_{4}$

$_{15}C_{4}$

Correct answer:

$_{15}P_{4}$

Explanation:

Order matters, so a permutation of 15 things chosen 4 at a time, or $_{15}P_{4}$ , is the correct answer.

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Example Question #63 : Probability

A bag of marbles consists of 13 green, 15 blue, 12 black and an unknown number of red marbles. If the chance of choosing a red marble is 1 in 3, how many marbles are there total?

Possible Answers:

$54$

$40$

$45$

$60$

$56$

Correct answer:

$60$

Explanation:

Adding the green, blue, and black marbles together gives 40. Then if there is a $\frac{1}{3}$ chance that a red marble is drawn, there must be an additional 20 marbles.

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Example Question #64 : Probability

Tiffany picks a peice of fruit from a bowl at random. The bowl contains 2 red delicious apples, 3 granny smith apples, 1 orange and 3 grapefruits. What is the probability that she chooses an apple?

Possible Answers:

$\frac{1}{9}$

$\frac{5}{9}$

$\frac{3}{9}$

$\frac{2}{9}$

$\frac{4}{9}$

Correct answer:

$\frac{5}{9}$

Explanation:

The chance she picks an apple is the total number of apples over the total number of fruits in the bowl. Since there are 2 kinds of apples, we add 2 red delicious and 3 granny smiths to get 5 apples total. In addition there are 4 more peices of fruit, so the total number of fruits is 9.

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Example Question #1511 : Psat Mathematics

In a bag, there are 6 black marbles and 8 yellow marbles. What is the possibility of choosing a yellow marble at random?

Possible Answers:

$\dpi{100} \small \frac{3}{7}$

$\dpi{100} \small \frac{4}{7}$

$\dpi{100} \small \frac{3}{4}$

$\dpi{100} \small \frac{4}{3}$

Correct answer:

$\dpi{100} \small \frac{4}{7}$

Explanation:

There is a total of 14 marbles, of which, 8 are yellow; therefore the probability of choosing a yellow marble is $\dpi{100} \small \frac{8}{14}$ or $\dpi{100} \small \frac{4}{7}$

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Example Question #1512 : Psat Mathematics

In a bag, there are 6 black and 8 yellow marbles. A yellow marble is chosen at random and is not replaced. What is the probability of choosing a second yellow marble?

Possible Answers:

$\dpi{100} \small \frac{7}{13}$

$\dpi{100} \small \frac{6}{7}$

$\dpi{100} \small \frac{4}{7}$

$\dpi{100} \small \frac{6}{13}$

Correct answer:

$\dpi{100} \small \frac{7}{13}$

Explanation:

Because a yellow marble was selected and not replaced, there is a total of 13 marbles in the bag and of which, 7 are yellow; therefore, the probability of selecting a yellow marble is $\dpi{100} \small \frac{7}{13}$

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PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #62 : How To Find The Probability Of An Outcome

Example Question #62 : Probability

Example Question #1511 : Psat Mathematics

Example Question #63 : How To Find The Probability Of An Outcome

Example Question #66 : How To Find The Probability Of An Outcome

Example Question #1512 : Psat Mathematics

Example Question #63 : Probability

Example Question #64 : Probability

Example Question #1511 : Psat Mathematics

Example Question #1512 : Psat Mathematics

All PSAT Math Resources

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