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PSAT Math : How to find the probability of an outcome

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Example Questions

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

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

Possible Answers:

$_{15}C_{4}$

$_{15}P_{4}$

$_{4}P_{15}$

$15!$

$_{4}C_{15}$

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 #183 : Data Analysis

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:

$60$

$45$

$54$

$56$

$40$

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 #184 : Data Analysis

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:

$\frac{5}{9}$

$\frac{3}{9}$

$\frac{1}{9}$

$\frac{2}{9}$

$\frac{4}{9}$

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 #185 : Data Analysis

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:

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

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

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

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

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 #71 : How To Find The Probability Of An Outcome

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:

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

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

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

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

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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Example Question #72 : How To Find The Probability Of An Outcome

A couple has four children. What is the probability of having exactly three girls?

Possible Answers:

$\frac{1}{8}$

$\frac{3}{4}$

$\frac{1}{4}$

$\frac{5}{8}$

$\frac{3}{16}$

Correct answer:

$\frac{1}{4}$

Explanation:

The total number of possibiliities is 16. The outcome we are looking for is three girls and one boy which happens only four times. Thus the probability becomes $\frac{4}{16}=\frac{1}{4}$ .

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Example Question #193 : Data Analysis

When a penny is flipped three times in a row, what is the probability of getting all heads or all tails?

Possible Answers:

$\frac{1}{4}$

$\frac{1}{8}$

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{3}{8}$

Correct answer:

$\frac{1}{4}$

Explanation:

The sample space for three coin tosses in a row is 8. Getting all heads can be done only one way. Getting all tails can be done only one way. So the probability of getting all heads or all tails is $\frac{2}{8}$ or $\frac{1}{4}$ .

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Example Question #194 : Data Analysis

A couple has three children. What is the probability of having exactly two girls or two boys?

Possible Answers:

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{8}$

$\frac{3}{8}$

$\frac{3}{4}$

Correct answer:

$\frac{3}{4}$

Explanation:

The sample space for three children is 8. We can count up what we want or subtract out what we don't want. What we don't want is all boys or all girls.

So the probability becomes $1 - \frac{2}{8} = \frac{6}{8} = \frac{3}{4}$

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Example Question #195 : Data Analysis

How many different ways can five books be lined up on a shelf?

Possible Answers:

130

150

120

Correct answer:

120

Explanation:

Order matters, so we use permutations. $_{5}^{5}\textrm{P}$ is $5\cdot 4\cdot 3\cdot 2\cdot 1 = 120$

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Example Question #72 : How To Find The Probability Of An Outcome

Jimmy is having trouble choosing what to wear to the baseball game. He has six shirts, three pants, two pairs of socks and three pairs of shoes. How many different outfits does Jimmy have to choose from?

Possible Answers:

150

108

125

Correct answer:

108

Explanation:

Choosing one of each clothing item is an independent event and should be multiplied together. So the answer becomes

$shirts\times pants\times socks\times shoes$

$6 \cdot 3 \cdot 2 \cdot 3 = 108$ different combinations.

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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 #62 : How To Find The Probability Of An Outcome

Example Question #183 : Data Analysis

Example Question #184 : Data Analysis

Example Question #185 : Data Analysis

Example Question #71 : How To Find The Probability Of An Outcome

Example Question #72 : How To Find The Probability Of An Outcome

Example Question #193 : Data Analysis

Example Question #194 : Data Analysis

Example Question #195 : Data Analysis

Example Question #72 : How To Find The Probability Of An Outcome

All PSAT Math Resources

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