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ISEE Lower Level Math : Outcomes

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10 Diagnostic Tests 170 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #61 : Probability

A bag has $\displaystyle 4$ red marbles, $\displaystyle 5$ green marbles, and $\displaystyle 6$ blue marbles. What is the probability of randomly drawing a red marble on the first draw?

Possible Answers:

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

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

$\frac{4}{15}$ $\displaystyle \frac{4}{15}$

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

Correct answer:

$\frac{4}{15}$ $\displaystyle \frac{4}{15}$

Explanation:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

$\text{Probability}=\frac{\text{Number of wanted outcomes}}{\text{Total number of outcomes}}$ $\displaystyle \text{Probability}=\frac{\text{Number of wanted outcomes}}{\text{Total number of outcomes}}$

For this question, we want a red marble. Since there are $\displaystyle 4$ red marbles, we have $\displaystyle 4$ wanted outcomes. Since there is a total of $\displaystyle 15$ marbles, we have a total of $\displaystyle 15$ possible outcomes.

The probability then becomes the following:

$\text{Probability}=\frac{4}{15}$ $\displaystyle \text{Probability}=\frac{4}{15}$

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Example Question #62 : Probability

A bag has $\displaystyle 4$ red marbles, $\displaystyle 5$ green marbles, and $\displaystyle 6$ blue marbles. What is the probability of randomly drawing a blue marble on the first draw?

Possible Answers:

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

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

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

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

Correct answer:

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

Explanation:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

For this question, we want a blue marble. Since there are $\displaystyle 6$ blue marbles, we have $\displaystyle 6$ wanted outcomes. Since there is a total of $\displaystyle 15$ marbles, we have a total of $\displaystyle 15$ possible outcomes.

The probability then becomes the following:

$\text{Probability}=\frac{6}{15}=\frac{2\cdot 3}{5\cdot 3}=\frac{2}{5}$ $\displaystyle \text{Probability}=\frac{6}{15}=\frac{2\cdot 3}{5\cdot 3}=\frac{2}{5}$

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Example Question #63 : Probability

A bag has $\displaystyle 4$ red marbles, $\displaystyle 5$ green marbles, and $\displaystyle 6$ blue marbles. What is the probability of randomly drawing a green marble on the first draw?

Possible Answers:

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

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

$\frac{7}{15}$ $\displaystyle \frac{7}{15}$

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

Correct answer:

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

Explanation:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

For this question, we want a green marble. Since there are $\displaystyle 5$ green marbles, we have $\displaystyle 5$ wanted outcomes. Since there is a total of $\displaystyle 15$ marbles, we have a total of $\displaystyle 15$ possible outcomes.

The probability then becomes the following:

$\text{Probability}=\frac{5}{15}=\frac{5\cdot 1}{5\cdot 3}=\frac{1}{3}$ $\displaystyle \text{Probability}=\frac{5}{15}=\frac{5\cdot 1}{5\cdot 3}=\frac{1}{3}$

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Example Question #64 : Probability

A bag has $\displaystyle 4$ red marbles, $\displaystyle 5$ green marbles, and $\displaystyle 6$ blue marbles. What is the probability of NOT drawing a blue marble on the first draw?

Possible Answers:

$\frac{1}{15}$ $\displaystyle \frac{1}{15}$

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

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

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

Correct answer:

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

Explanation:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

For this question, we do not want a blue marble. This means that we are trying to find the proability of drawing either a red or a green marble. Since we have $\displaystyle 4$ red marbles and $\displaystyle 5$ green marbles, we have $\displaystyle 9$ wanted outcomes. Since there is a total of $\displaystyle 15$ marbles, we have a total of $\displaystyle 15$ possible outcomes.

The probability then becomes the following:

$\text{Probability}=\frac{9}{15}=\frac{3\cdot 3}{3\cdot 5}=\frac{3}{5}$ $\displaystyle \text{Probability}=\frac{9}{15}=\frac{3\cdot 3}{3\cdot 5}=\frac{3}{5}$

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Example Question #65 : Probability

A bag has $\displaystyle 4$ red marbles, $\displaystyle 5$ green marbles, and $\displaystyle 6$ blue marbles. What is the probability of NOT drawing a green marble on the first draw?

Possible Answers:

$\frac{14}{15}$ $\displaystyle \frac{14}{15}$

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

$\frac{13}{15}$ $\displaystyle \frac{13}{15}$

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

Correct answer:

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

Explanation:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

For this question, we do not want a green marble. This means that we are trying to find the proability of drawing either a blue or a green marble. Since we have $\displaystyle 6$ blue marbles and $\displaystyle 4$ red marbles, we have $\displaystyle 10$ wanted outcomes. Since there is a total of $\displaystyle 15$ marbles, we have a total of $\displaystyle 15$ possible outcomes.

The probability then becomes the following:

$\text{Probability}=\frac{10}{15}=\frac{2\cdot 5}{3\cdot 5}=\frac{2}{3}$ $\displaystyle \text{Probability}=\frac{10}{15}=\frac{2\cdot 5}{3\cdot 5}=\frac{2}{3}$

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Example Question #61 : Probability

If you randomly choose a number between $\displaystyle 1$ and $\displaystyle 10$, inclusive, what is the proability the chosen number is even?

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

First, write down the possible wanted outcomes:

$\displaystyle 2, 4, 6, 8, 10$

Now, because there are $\displaystyle 5$ even numbers, we have $\displaystyle 5$ wanted outcomes.

Since we are choosing numbers between $\displaystyle 1$ and $\displaystyle 10$, inclusive, we have a $\displaystyle 10$ total outcomes.

The probability then can be written as the following:

$\text{Probability}=\frac{5}{10}=\frac{5\cdot 1}{5\cdot 2}=\frac{1}{2}$ $\displaystyle \text{Probability}=\frac{5}{10}=\frac{5\cdot 1}{5\cdot 2}=\frac{1}{2}$

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Example Question #67 : Probability

If you randomly choose a number between $1\text{ and }10$ $\displaystyle 1\text{ and }10$, inclusive, what is the probability that the number is divisible by $\displaystyle 4$?

Possible Answers:

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

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

$\frac{2}{9}$ $\displaystyle \frac{2}{9}$

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

Correct answer:

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

Explanation:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

First, write down the possible wanted outcomes:

4, 8 $\displaystyle 4, 8$

Now, because there are $\displaystyle 2$ numbers divisible by four, we have $\displaystyle 2$ wanted outcomes.

Since we are choosing numbers between $\displaystyle 1$ and $\displaystyle 10$, inclusive, we have a $\displaystyle 10$ total outcomes.

The probability then can be written as the following:

$\text{Probability}=\frac{2}{10}=\frac{2\cdot 1}{2\cdot 5}=\frac{1}{5}$ $\displaystyle \text{Probability}=\frac{2}{10}=\frac{2\cdot 1}{2\cdot 5}=\frac{1}{5}$

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Example Question #68 : Probability

If you randomly choose a number between $1\text{ and }10$ $\displaystyle 1\text{ and }10$, inclusive, what is the probability that the number is less than $\displaystyle 9$, but greater than $\displaystyle 3$?

Possible Answers:

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

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

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

$\frac{7}{10}$ $\displaystyle \frac{7}{10}$

Correct answer:

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

Explanation:

Recall that a probability is the likelihood of something occurring.

Mathematically, we can write probability as the following:

First, write down the possible wanted outcomes:

$\displaystyle 4, 5, 6, 7, 8$

Now, because there are $\displaystyle 5$ numbers that fit the criteria, we have $\displaystyle 5$ wanted outcomes.

Since we are choosing numbers between $\displaystyle 1$ and $\displaystyle 10$, inclusive, we have a $\displaystyle 10$ total outcomes.

The probability then can be written as the following:

$\text{Probability}=\frac{5}{10}=\frac{5\cdot 1}{5\cdot 2}=\frac{1}{2}$ $\displaystyle \text{Probability}=\frac{5}{10}=\frac{5\cdot 1}{5\cdot 2}=\frac{1}{2}$

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Example Question #69 : Probability

If the probability of winning your next baseball game is p=0.73 $\displaystyle p=0.73$, what is the probability that you do not win?

Possible Answers:

0.01 $\displaystyle 0.01$

0.75 $\displaystyle 0.75$

0.27 $\displaystyle 0.27$

0.5 $\displaystyle 0.5$

0.8 $\displaystyle 0.8$

Correct answer:

0.27 $\displaystyle 0.27$

Explanation:

The probability of an event not happening is one minus the probability it does happen.

Since the probability of winning the game is 0.73 $\displaystyle 0.73$, then the probability of not winning would be,

$\\P_{lose}=1-P_{win} \\P_{lose}=1-0.73 \\P_{lose}=0.27$ $\displaystyle \\P_{lose}=1-P_{win} \\P_{lose}=1-0.73 \\P_{lose}=0.27$ .

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Example Question #70 : Probability

If you have $\displaystyle 5$ gold fish and $\displaystyle 3$ beta fish, what is the probability you pick a beta fish if you randomly select one from you tank?

Possible Answers:

$\frac{3}{8}$ $\displaystyle \frac{3}{8}$

$\frac{8}{3}$ $\displaystyle \frac{8}{3}$

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

$\frac{5}{3}$ $\displaystyle \frac{5}{3}$

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

Correct answer:

$\frac{3}{8}$ $\displaystyle \frac{3}{8}$

Explanation:

To the probability of selecting a particular fish is the number of that fish divided by the total possible fish to choose from.

The total is $\displaystyle 5$ gold fish plus $\displaystyle 3$ beta fish or $\displaystyle 8$.

So the probability of selecting a beta fish is

$P=\frac{beta}{all\ fish}=\frac{3}{5+3}=\frac{3}{8}$ $\displaystyle P=\frac{beta}{all\ fish}=\frac{3}{5+3}=\frac{3}{8}$.

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ISEE Lower Level Math : Outcomes

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

All ISEE Lower Level Math Resources

Example Questions

Example Question #61 : Probability

Example Question #62 : Probability

Example Question #63 : Probability

Example Question #64 : Probability

Example Question #65 : Probability

Example Question #61 : Probability

Example Question #67 : Probability

Example Question #68 : Probability

Example Question #69 : Probability

Example Question #70 : Probability

All ISEE Lower Level Math Resources

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