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PSAT Math : How to find the probability of an outcome

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Example Questions

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 #53 : Outcomes

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

Possible Answers:

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

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

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

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

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

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 : Outcomes

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

Possible Answers:

$\frac{1}{16}$

$\frac{7}{16}$

$\frac{5}{16}$

$\frac{3}{8}$

$\frac{1}{2}$

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 #61 : How To Find The Probability Of An Outcome

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:

$\frac{1}{80}$

$\frac{1}{85}$

$\frac{1}{84}$

$\frac{1}{90}$

$\frac{1}{64}$

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:

$20\%$

$55\%$

$50\%$

$70\%$

$60\%$

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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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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PSAT Math : How to find the probability of an outcome

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

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

Example Question #58 : Probability

Example Question #59 : Probability

Example Question #53 : Outcomes

Example Question #61 : Outcomes

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 #66 : How To Find The Probability Of An Outcome

All PSAT Math Resources

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