# ISEE Middle Level Math : Probability

## Example Questions

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

Find the probability that we draw a 4 of Hearts from a deck of cards.

Explanation:

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

So, given the event of drawing a 4 of Hearts, we can calculate the following:

Because there is only one 4 of Hearts in a deck of cards.

Now, we can calculate the following:

Because there are 52 cards we could potentially draw from a deck of cards.

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

Therefore, the probability of drawing a 4 of Hearts from a deck of cards is .

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

A bag contains the following:

• 5 pens
• 6 pencils
• 7 markers

Find the probability of drawing a pencil from the bag.

Explanation:

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

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

Because there are 6 pencils in the bag.

Now, we can calculate the following:

Because there are 18 total items in the bag:

• 5 pens
• 6 pencils
• 7 markers

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

Therefore, the probability of drawing a pencil from the bag is .

### Example Question #563 : Data Analysis And Probability

A bag contains the following:

• 10 red pens
• 15 black pens
• 5 blue pens

Find the probability of drawing a black pen.

Explanation:

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

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

Because there are 15 black pens in the bag.

Now, we can calculate the following:

Because there are 30 total items in the bag to choose from:

• 10 red pens
• 15 black pens
• 5 blue pens

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

Therefore, the probability of drawing a black pen from the bag is .

### Example Question #61 : Probability

Find the probability of drawing a 3 from a deck of cards.

Explanation:

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

So, given the event of drawing a 3 from a deck of cards, we can calculate the following:

Beause there are four 3s we could draw from a deck of cards

•          3 of hearts
•          3 of diamonds
•          3 of clubs

Now we can calculate the following:

Because there are 52 cards in the deck we could potentially draw.

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

### Example Question #881 : Isee Middle Level (Grades 7 8) Mathematics Achievement

A bag contains the following:

•          8 red crayons
•          7 blue crayons
•          4 green crayons
•          5 yellow crayons

Find the probability you grab a green crayon from the bag.

Explanation:

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

Now, given the event of grabbing  a green crayon from the bag, we can calculate the following:

Because there are 4 green crayons in the bag.

We can also calculate the following:

Because there are 24 total crayons we could potentially grab from the bag.

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

Therefore, the probability of grabbing a green crayon is .

### Example Question #61 : Outcomes

A classroom contains the following:

• 24 girls
• 32 boys

Find the probability the teacher calls on a girl.

Explanation:

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

Now, given the event of calling on a girl, we can determine:

because there are 24 girls in the class the teacher could call on.

We can determine:

because there are 56 total students in the class the teacher could potentially call on:

• 24 girls
• 32 boys

Now, we can substitute into the formula.  We get

Therefore, the probability the teacher calls on a girl is .

### Example Question #64 : How To Find The Probability Of An Outcome

Find the probability of drawing a 7 from a deck of cards.

Explanation:

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

So, given the event of drawing a 7 from a deck of cards we can calculate the following:

because there are four ways we can draw a 7 from the deck:

• 7 of clubs
• 7 of hearts
• 7 of diamonds

Now, we can calculate the following:

because there are 52 cards we could potentially draw from a deck of cards.

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

Therefore, the probability of drawing a 7 from a deck of cards is .

### Example Question #571 : Data Analysis And Probability

Find the probability of drawing a heart from a deck of cards.

Explanation:

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

So, given the event of drawing heart, we can calculate the following:

because there are 13 ways we can draw a heart:

• Ace
• Two
• Three
• Four
• Five
• Six
• Seven
• Eight
• Nine
• Ten
• Jack
• Queen
• King

Now, we can calculate the following:

because there are 52 cards we could potentially draw from a deck of cards.

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

Therefore, the probability of drawing a heart from a deck of cards is .

### Example Question #62 : Outcomes

A box contains the following:

• 9 blue crayons
• 3 green crayons
• 4 red crayons
• 1 yellow crayon

Find the probability of grabbing a red crayon from the box.

Explanation:

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

Now, given the event of grabbing a red crayon from the box, we can calculate:

because there are 4 red crayons in the box we could grab.

We can also calculate:

because there are 17 total crayons we could potentially grab:

• 9 blue crayons
• 3 green crayons
• 4 red crayons
• 1 yellow crayon

So, we get

Therefore, the probability of grabbing a red crayon from the box is .

### Example Question #61 : Probability

Find the probability that we draw a 5 from a deck of cards.

Explanation:

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

So, given the event of drawing a 5, we can calculate the following:

because there are 4 ways we can draw a 5 from a deck:

•          5 of clubs
•          5 of hearts
•          5 of diamonds

Now, we can calculate the following:

because there are 52 cards we could potentially draw from a deck of cards.

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

Therefore, the probability of drawing a 5 from a deck of cards is .