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ISEE Lower Level Math : Probability

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Example Questions

Example Question #81 : How To Find The Probability Of An Outcome

If a class has 10 boys and 12 girls, what is the probability the teacher will call on a boy?

Possible Answers:

$\displaystyle 12$

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

$\frac{5}{11}$ $\displaystyle \frac{5}{11}$

$\displaystyle 10$

$\frac{10}{12}$ $\displaystyle \frac{10}{12}$

Correct answer:

$\frac{5}{11}$ $\displaystyle \frac{5}{11}$

Explanation:

To find the probability of an event, we will use the following formula:

$\text{probability of an event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$ $\displaystyle \text{probability of an event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$

Now, in the event of calling on a boy in the class, we can determine the number of ways the event can happen:

$\text{number of ways event can happen} = 10$ $\displaystyle \text{number of ways event can happen} = 10$

because there are 10 boy students in the class.

To find the number of possible outcomes, we get

$\text{total number of possible outcomes} = 22$ $\displaystyle \text{total number of possible outcomes} = 22$

because there are 22 total students the teacher could potentially call on.

Knowing all of this, we can substitute into the formula. We get

$\text{probability of calling on a boy} = \frac{10}{22}$ $\displaystyle \text{probability of calling on a boy} = \frac{10}{22}$

$\text{probability of calling on a boy} = \frac{5}{11}$ $\displaystyle \text{probability of calling on a boy} = \frac{5}{11}$

Therefore, the probability of calling on a boy is $\frac{5}{11}$ $\displaystyle \frac{5}{11}$.

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Example Question #82 : How To Find The Probability Of An Outcome

If a class has 10 boys and 12 girls, what is the probability the teacher will call on a girl?

Possible Answers:

$\displaystyle 12$

$\frac{12}{10}$ $\displaystyle \frac{12}{10}$

$\frac{6}{11}$ $\displaystyle \frac{6}{11}$

$\displaystyle 10$

$\frac{1}{12}$ $\displaystyle \frac{1}{12}$

Correct answer:

$\frac{6}{11}$ $\displaystyle \frac{6}{11}$

Explanation:

To find the probability of an event, we will use the following formula:

Now, in the event of calling on a girl in the class, we can determine the number of ways the event can happen:

$\text{number of ways event can happen} = 12$ $\displaystyle \text{number of ways event can happen} = 12$

because there are 12 girl students in the class.

To find the number of possible outcomes, we get

$\text{total number of possible outcomes} = 22$ $\displaystyle \text{total number of possible outcomes} = 22$

because there are 22 total students the teacher could potentially call on.

Knowing all of this, we can substitute into the formula. We get

$\text{probability of calling on a girl} = \frac{12}{22}$ $\displaystyle \text{probability of calling on a girl} = \frac{12}{22}$

$\text{probability of calling on a girl} = \frac{6}{11}$ $\displaystyle \text{probability of calling on a girl} = \frac{6}{11}$

Therefore, the probability of calling on a girl is $\frac{6}{11}$ $\displaystyle \frac{6}{11}$.

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Example Question #81 : How To Find The Probability Of An Outcome

A box contains the following:

2 red marbles
1 blue marbles
3 green marbles

What is the probability of picking a green marble?

Possible Answers:

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

$\displaystyle 3$

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

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

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

Correct answer:

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

Explanation:

To find the probability of an event, we will use the following formula:

$\text{probability of event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$ $\displaystyle \text{probability of event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$

Now, given the event of drawing a green marble, we can calculate the following.

$\text{number of ways event can happen} = 3$ $\displaystyle \text{number of ways event can happen} = 3$

because there are 3 green marbles that we can pick.

Now, we can calculate the following.

$\text{total number of possible outcomes} = 6$ $\displaystyle \text{total number of possible outcomes} = 6$

because there are 6 total different marbles we could potentially pick.

Knowing this, we can substitute into the formula.

$\text{probability of picking a green marble} = \frac{3}{6}$ $\displaystyle \text{probability of picking a green marble} = \frac{3}{6}$

$\text{probability of picking a green marble} = \frac{1}{2}$ $\displaystyle \text{probability of picking a green marble} = \frac{1}{2}$

Therefore, the probability of picking a green marble from the box is $\frac{1}{2}$ $\displaystyle \frac{1}{2}$.

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Example Question #81 : How To Find The Probability Of An Outcome

There are 10 bottles of water and 8 bottles of juice in the refrigerator.

What is the probability of grabbing a bottle of water?

Possible Answers:

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

$\frac{2}{10}$ $\displaystyle \frac{2}{10}$

$\frac{10}{8}$ $\displaystyle \frac{10}{8}$

$\displaystyle 10$

$\frac{5}{9}$ $\displaystyle \frac{5}{9}$

Correct answer:

$\frac{5}{9}$ $\displaystyle \frac{5}{9}$

Explanation:

To find the probability of an event, we will use the following formula:

Now, given the event of grabbing a bottle of water, we can calculate the following.

$\text{number of ways event can happen} = 10$ $\displaystyle \text{number of ways event can happen} = 10$

because there are 10 bottles of water we can grab.

Now, we can calculate the following.

$\text{total number of possible outcomes} = 18$ $\displaystyle \text{total number of possible outcomes} = 18$

because there are 18 total bottles in the refrigerator (10 water + 8 juice = 18 total).

Knowing this, we can substitute into the formula.

$\text{probability of grabbing a bottle of water} = \frac{10}{18}$ $\displaystyle \text{probability of grabbing a bottle of water} = \frac{10}{18}$

$\text{probability of grabbing a bottle of water} = \frac{5}{9}$ $\displaystyle \text{probability of grabbing a bottle of water} = \frac{5}{9}$

Therefore, the probability of picking a green marble from the box is $\frac{5}{9}$ $\displaystyle \frac{5}{9}$.

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Example Question #83 : How To Find The Probability Of An Outcome

A classroom contains the following students:

10 girls
13 boys

Find the probability the teacher calls on a girl.

Possible Answers:

$\displaystyle 10$

$\frac{10}{13}$ $\displaystyle \frac{10}{13}$

$\displaystyle 13$

$\frac{10}{23}$ $\displaystyle \frac{10}{23}$

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

Correct answer:

$\frac{10}{23}$ $\displaystyle \frac{10}{23}$

Explanation:

To find the probability of an event, we will use the following formula:

Now, given the event of the teacher calling on a girl, we can calculate the following:

$\text{number of ways event can happen} = 10$ $\displaystyle \text{number of ways event can happen} = 10$

because there are 10 girls in the classroom.

Now, we can calculate the following:

$\text{total number of possible outcomes} = 23$ $\displaystyle \text{total number of possible outcomes} = 23$

because there are 23 total students the teacher could potentially call on:

10 girls
13 boys

$\displaystyle 10+13=23$

Knowing this, we can substitute into the formula. We get

$\text{probability of calling on a girl} = \frac{10}{23}$ $\displaystyle \text{probability of calling on a girl} = \frac{10}{23}$

Therefore, the probability of the teacher calling on a girl is $\frac{10}{23}$ $\displaystyle \frac{10}{23}$

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Example Question #84 : How To Find The Probability Of An Outcome

A bag contains the following:

2 red pens
3 blue pens
2 black pens

What is the probability of grabbing a black pen from the bag?

Possible Answers:

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

$\displaystyle 2$

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

$\frac{3}{7}$ $\displaystyle \frac{3}{7}$

$\frac{2}{7}$ $\displaystyle \frac{2}{7}$

Correct answer:

$\frac{2}{7}$ $\displaystyle \frac{2}{7}$

Explanation:

To find the probability of an event, we will use the following formula:

Now, given the event of grabbing a black pen from the bag, we can calculate the following:

$\text{number of ways event can happen} = 2$ $\displaystyle \text{number of ways event can happen} = 2$

because there are 2 black pens in the bag.

Now, we can calculate the following:

$\text{total number of possible outcomes} = 7$ $\displaystyle \text{total number of possible outcomes} = 7$

because there are 7 objects in the bag we could potentially grab:

2 red pens
3 blue pens
2 black pens

2+3+2=7 $\displaystyle 2+3+2=7$

Knowing this, we can substitute into the formula. We get

$\text{probability of grabbing a black pen} = \frac{2}{7}$ $\displaystyle \text{probability of grabbing a black pen} = \frac{2}{7}$

Therefore, the probability of grabbing a black pen from the bag is $\frac{2}{7}$ $\displaystyle \frac{2}{7}$.

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Example Question #621 : Isee Lower Level (Grades 5 6) Mathematics Achievement

A bag contains the following:

3 blue pens
5 black pens
7 red pens

Find the probability of drawing a black pen from the bag.

Possible Answers:

$\displaystyle 5$

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

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

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

$\frac{5}{10}$ $\displaystyle \frac{5}{10}$

Correct answer:

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

Explanation:

To find the probability of an event, we will use the following formula:

So, given the event of drawing a black pen from a bag, we can calculate the following:

$\text{number of ways event can happen} = 5$ $\displaystyle \text{number of ways event can happen} = 5$

because there are 5 black pens in the bag we can choose from.

Now, we can calculate the following:

$\text{total number of possible outcomes} = 15$ $\displaystyle \text{total number of possible outcomes} = 15$

because there are 15 total objects in the bag we could potentially draw:

3 blue pens
5 black pens
7 red pens

$\displaystyle 3+5+7=15$

Knowing this, we can substitute into the formula. We get

$\text{probability of drawing black pen} = \frac{5}{15}$ $\displaystyle \text{probability of drawing black pen} = \frac{5}{15}$

$\text{probability of drawing black pen} = \frac{1}{3}$ $\displaystyle \text{probability of drawing black pen} = \frac{1}{3}$

Therefore, the probability of drawing a black pen from a bag is $\frac{1}{3}$ $\displaystyle \frac{1}{3}$.

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Example Question #81 : How To Find The Probability Of An Outcome

A classroom contains the following:

6 black chairs
7 blue chairs
2 red chairs

Find the probability you will sit in a red chair.

Possible Answers:

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

$\frac{2}{15}$ $\displaystyle \frac{2}{15}$

$\frac{2}{13}$ $\displaystyle \frac{2}{13}$

$\displaystyle 2$

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

Correct answer:

$\frac{2}{15}$ $\displaystyle \frac{2}{15}$

Explanation:

To find the probability of an event, we will use the following formula:

So, given the event of sitting in a red chair, we can calculate the following:

$\text{number of ways event can happen} = 2$ $\displaystyle \text{number of ways event can happen} = 2$

because there are 2 red chairs in the classroom.

Now, we can calculate the following:

$\text{total number of possible outcomes} = 15$ $\displaystyle \text{total number of possible outcomes} = 15$

because there are 15 different chairs we could potentially sit on.

6 black chairs
7 blue chairs
2 red chairs

$\displaystyle 6+7+2=15$

Knowing this, we can substitute into the formula. We get

$\text{probability of sitting in a red chair} = \frac{2}{15}$ $\displaystyle \text{probability of sitting in a red chair} = \frac{2}{15}$

Therefore, the probability of sitting in a red chair is $\frac{2}{15}$ $\displaystyle \frac{2}{15}$.

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Example Question #85 : How To Find The Probability Of An Outcome

A bag contains the following:

3 red pens
5 blue pens
6 black pens

Find the probability of grabbing a blue pen from the bag.

Possible Answers:

$\frac{5}{14}$ $\displaystyle \frac{5}{14}$

$\frac{1}{14}$ $\displaystyle \frac{1}{14}$

$\displaystyle 5$

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

$\frac{1}{9}$ $\displaystyle \frac{1}{9}$

Correct answer:

$\frac{5}{14}$ $\displaystyle \frac{5}{14}$

Explanation:

To find the probability of an event, we will use the following formula:

Given the event of grabbing a blue pen from the bag, we can determine

$\text{number of ways event can happen} = 5$ $\displaystyle \text{number of ways event can happen} = 5$

because there are 5 blue pens in the bag.

$\text{total number of possible outcomes} = 14$ $\displaystyle \text{total number of possible outcomes} = 14$

because there are 14 total pens in the bag we could potentially grab:

3 red pens
5 blue pens
6 black pens

$\displaystyle 3+5+6=14$

Now, we can substitute into the formula. We get

$\text{probability of grabbing a blue pen} = \frac{5}{14}$ $\displaystyle \text{probability of grabbing a blue pen} = \frac{5}{14}$

Therefore, the probability of grabbing a blue pen from the bag is $\frac{5}{14}$ $\displaystyle \frac{5}{14}$.

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Example Question #81 : Data Analysis And Probability

A bag contains the following:

2 blue pens
3 black pens
1 red pen

Find the probability of grabbing a red pen from the bag.

Possible Answers:

$\displaystyle 1$

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

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

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

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

Correct answer:

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

Explanation:

To find the probability of an event, we will use the following formula:

So, given the event of grabbing a red pen from the bag, we can calculate:

$\text{number of ways event can happen} = 1$ $\displaystyle \text{number of ways event can happen} = 1$

because there is only 1 pen that we could grab from the bag.

We can also calculate the following:

$\text{total number of possible outcomes} = 6$ $\displaystyle \text{total number of possible outcomes} = 6$

because there are 6 pens we could potentially grab (2 blue + 3 black + 1 red = 6 pens).

Now, we can substitute into the formula. We get

$\text{probability of grabbing a red pen} = \frac{1}{6}$ $\displaystyle \text{probability of grabbing a red pen} = \frac{1}{6}$

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ISEE Lower Level Math : Probability

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

All ISEE Lower Level Math Resources

Example Questions

Example Question #81 : How To Find The Probability Of An Outcome

Example Question #82 : How To Find The Probability Of An Outcome

Example Question #81 : How To Find The Probability Of An Outcome

Example Question #81 : How To Find The Probability Of An Outcome

Example Question #83 : How To Find The Probability Of An Outcome

Example Question #84 : How To Find The Probability Of An Outcome

Example Question #621 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Example Question #81 : How To Find The Probability Of An Outcome

Example Question #85 : How To Find The Probability Of An Outcome

Example Question #81 : Data Analysis And Probability

All ISEE Lower Level Math Resources

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