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ISEE Lower Level Quantitative : Data Analysis and Probability

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

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All ISEE Lower Level Quantitative Resources

20 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : How To Find The Probability Of An Outcome

A bag contains differently colored balls. In it are $\displaystyle 5$ pink balls, $\displaystyle 6$ red balls, and $\displaystyle 4$ green balls. What is the probability of choosing a red ball at random?

Possible Answers:

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Correct answer:

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

Explanation:

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are $\displaystyle 6$ red balls and a total of $\displaystyle 15$ balls in the bag. This is represented as the fraction: $\tfrac{6}{15}$ $\displaystyle \tfrac{6}{15}$. This can be reduced to $\tfrac{2}{5}$ $\displaystyle \tfrac{2}{5}$. The answer is $\tfrac{2}{5}$ $\displaystyle \tfrac{2}{5}$.

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Example Question #32 : How To Find The Probability Of An Outcome

Possible Answers:

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Correct answer:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Explanation:

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are $\displaystyle 5$ red balls and a total of $\displaystyle 15$ balls in the bag. This is represented as the fraction: $\tfrac{5}{15}$ $\displaystyle \tfrac{5}{15}$. This can be reduced to $\tfrac{1}{3}$ $\displaystyle \tfrac{1}{3}$. The answer is $\tfrac{1}{3}$ $\displaystyle \tfrac{1}{3}$.

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Example Question #32 : How To Find The Probability Of An Outcome

A game requires you to throw a ball at some randomly-arranged colored tiles in order to win a prize. There are $\displaystyle 20$ white tiles, $\displaystyle 15$ blue tiles, $\displaystyle 10$ red tiles, and $\displaystyle 5$ black tiles. What is the probability of hitting a black tile?

Possible Answers:

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\frac{1}{20}$ $\displaystyle \frac{1}{20}$

$\frac{1}{50}$ $\displaystyle \frac{1}{50}$

$\frac{1}{10}$ $\displaystyle \frac{1}{10}$

Correct answer:

$\frac{1}{10}$ $\displaystyle \frac{1}{10}$

Explanation:

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are $\displaystyle 5$ black tiles and a total of $\displaystyle 50$ tiles. This is represented as the fraction: $\tfrac{5}{50}$ $\displaystyle \tfrac{5}{50}$. This can be reduced to $\tfrac{1}{10}$ $\displaystyle \tfrac{1}{10}$. The answer is $\tfrac{1}{10}$ $\displaystyle \tfrac{1}{10}$.

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Example Question #32 : How To Find The Probability Of An Outcome

Misha is choosing movies from a bin at a store. In the bin are $\displaystyle 20$ action movies, $\displaystyle 20$ comedies, $\displaystyle 10$ documentaries, and $\displaystyle 10$ other types of films. If she chooses randomly, what is the probability that Misha will pick out a comedy movie?

Possible Answers:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{5}{6}$ $\displaystyle \frac{5}{6}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

Correct answer:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Explanation:

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are $\displaystyle 20$ comedy movies and a total of $\displaystyle 60$ movies. This is represented as the fraction: $\tfrac{20}{60}$ $\displaystyle \tfrac{20}{60}$. This can be reduced to $\tfrac{1}{3}$ $\displaystyle \tfrac{1}{3}$. The answer is $\tfrac{1}{3}$ $\displaystyle \tfrac{1}{3}$.

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Example Question #31 : Outcomes

Jessica has a box of chocolates. $\displaystyle 5$ have buttercream filling, $\displaystyle 3$ have cherry filling, $\displaystyle 2$ have raspberry filling, $\displaystyle 5$ have coconut filling, and $\displaystyle 5$ have no filling. What is the probability of Jessica choosing a chocolate with no filling?

Possible Answers:

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

Correct answer:

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

Explanation:

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are $\displaystyle 5$ chocolates with no filling and a total of $\displaystyle 20$ chocolates. This is represented as the fraction: $\tfrac{5}{20}$ $\displaystyle \tfrac{5}{20}$. This can be reduced to $\tfrac{1}{4}$ $\displaystyle \tfrac{1}{4}$. The answer is $\tfrac{1}{4}$ $\displaystyle \tfrac{1}{4}$.

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Example Question #31 : Data Analysis And Probability

A group of kids are playing duck-duck-goose. In the circle sit $\displaystyle 8$ third graders, $\displaystyle 4$ fourth graders, and $\displaystyle 4$ fifth graders. What is the probability that a third or fourth grader will be chosen?

Possible Answers:

$\frac{1}{8}$ $\displaystyle \frac{1}{8}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

Correct answer:

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

Explanation:

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are $\displaystyle 12$ third and fourth graders and a total of $\displaystyle 16$ students. This is represented as the fraction: $\tfrac{12}{16}$ $\displaystyle \tfrac{12}{16}$. This can be reduced to $\tfrac{3}{4}$ $\displaystyle \tfrac{3}{4}$. The answer is $\tfrac{3}{4}$ $\displaystyle \tfrac{3}{4}$.

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Example Question #34 : How To Find The Probability Of An Outcome

A jar contains $\displaystyle 3$ candy bars, $\displaystyle 2$ lollipops, and $\displaystyle 5$ other types of sweets. What is the probability of drawing a lollipop at random from the jar?

Possible Answers:

$\frac{3}{10}$ $\displaystyle \frac{3}{10}$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Correct answer:

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

Explanation:

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are $\displaystyle 2$ lollipops and a total of $\displaystyle 10$ pieces of candy. This is represented as the fraction: $\tfrac{2}{10}$ $\displaystyle \tfrac{2}{10}$. This can be reduced to $\tfrac{1}{5}$ $\displaystyle \tfrac{1}{5}$. The answer is $\tfrac{1}{5}$ $\displaystyle \tfrac{1}{5}$.

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Example Question #35 : How To Find The Probability Of An Outcome

Jacob has $\displaystyle 3$ mechanical pencils, $\displaystyle 10$ colored pencils, and $\displaystyle 2$ erasers in his bag. What is the probability of him taking out a colored pencil at random from the bag?

Possible Answers:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

Correct answer:

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

Explanation:

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are $\displaystyle 10$ colored pencils and a total of $\displaystyle 15$ items. This is represented as the fraction: $\tfrac{10}{15}$ $\displaystyle \tfrac{10}{15}$. This can be reduced to $\tfrac{2}{3}$ $\displaystyle \tfrac{2}{3}$. The answer is $\tfrac{2}{3}$ $\displaystyle \tfrac{2}{3}$.

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Example Question #32 : Outcomes

If Justin rolls a six-sided die, what is the probability of it landing on an even number?

Possible Answers:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\displaystyle 2$

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Correct answer:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Explanation:

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are $\displaystyle 3$ even numbers and a total of $\displaystyle 6$ numbers on the die. This is represented as the fraction: $\tfrac{3}{6}$ $\displaystyle \tfrac{3}{6}$. This can be reduced to $\tfrac{1}{2}$ $\displaystyle \tfrac{1}{2}$. The answer is $\tfrac{1}{2}$ $\displaystyle \tfrac{1}{2}$.

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Example Question #31 : Probability

A store has a bin of books on sale. In the bin, there are $\displaystyle 10$ novels, $\displaystyle 6$ comic books, $\displaystyle 5$ reference books, and $\displaystyle 4$ picture books. What is the probability that someone will choose a novel from the bin?

Possible Answers:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

${}\frac{1}{10}$ $\displaystyle {}\frac{1}{10}$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

Correct answer:

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

Explanation:

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are $\displaystyle 10$ novels and a total of $\displaystyle 25$ books. This is represented as the fraction: $\tfrac{10}{25}$ $\displaystyle \tfrac{10}{25}$. This can be reduced to $\tfrac{2}{5}$ $\displaystyle \tfrac{2}{5}$. The answer is $\tfrac{2}{5}$ $\displaystyle \tfrac{2}{5}$.

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All ISEE Lower Level Quantitative Resources

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ISEE Lower Level Quantitative : Data Analysis and Probability

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #31 : How To Find The Probability Of An Outcome

Example Question #32 : How To Find The Probability Of An Outcome

Example Question #32 : How To Find The Probability Of An Outcome

Example Question #32 : How To Find The Probability Of An Outcome

Example Question #31 : Outcomes

Example Question #31 : Data Analysis And Probability

Example Question #34 : How To Find The Probability Of An Outcome

Example Question #35 : How To Find The Probability Of An Outcome

Example Question #32 : Outcomes

Example Question #31 : Probability

All ISEE Lower Level Quantitative Resources

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