# ISEE Middle Level Math : How to find the probability of an outcome

## Example Questions

### Example Question #41 : Probability

A large box contains some balls, each of which is marked with a number; one ball is marked with a "1", two balls are marked with a "2". and so forth up to ten balls with a "10". A blank ball is also included.

Give the probability that a ball drawn at random will NOT be an even-numbered ball.

Explanation:

The number of balls in the box is

.

The number of even-numbered balls is

leaving  balls without even numbers. This makes the probability of not drawing an even-numbered ball

.

### Example Question #543 : Data Analysis And Probability

Find the probability of drawing an 8 from a deck of cards.

Explanation:

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

Now, given the event of drawing an 8 from a deck of cards, we can calculate the number of ways the event can happen.  We get

because there are 4 different ways we can draw 8 from a deck of cards:

2. 8 of clubs
3. 8 of hearts
4. 8 of diamonds

Now, we can determine the total number of possible outcomes.  We get

because there are 52 different cards we could possibly draw from a deck of cards.  Knowing this, we can substitute into the formula.  We get

Now, we can simplify.

Therefore, the probability of drawing an 8 from a deck of cards is

### Example Question #544 : Data Analysis And Probability

If there are 12 boys and 14 girls in a class, what is the probability the teacher will call 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 in the class, we can calculate the number of ways the event can happen.  We get

because there are 14 girls in the classroom.

Now, we can determine the total number of possible outcomes.  We get

because there are 26 different students the teacher could possibly call on:

• 12 boys
• 14 girls

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

Now, we can simplify.

Therefore, the probability of calling on a girl in class is

### Example Question #41 : Outcomes

Find the probability of drawing a diamond card from a deck of cards.

Explanation:

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

So, given the event of drawing a diamond card from a deck of cards, we get

because there are 13 diamond cards in a deck of cards:

1. Ace of diamonds
2. Two of diamonds
3. Three of diamonds
4. Four of diamonds
5. Five of diamonds
6. Six of diamonds
7. Seven of diamonds
8. Eight of diamonds
9. Nine of diamonds
10. Ten of diamonds
11. Jack of diamonds
12. Queen of diamonds
13. King of diamonds

Now, we will find the total number of possible outcomes.  We get

because there are 52 cards to choose from within one deck.

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

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

### Example Question #42 : Probability

Find the probability of drawing a black card from a deck of cards.

Explanation:

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

So, given the event of drawing a black card from a deck of cards, we get

because there are 26 black cards cards in a deck of cards:

• 13 cards that are Spades
• 13 cards that are Clubs

Now, we will find the total number of possible outcomes.  We get

because there are 52 cards to choose from within one deck.

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

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

### Example Question #45 : Develop And Compare Probability Models And Find Probabilities Of Events: Ccss.Math.Content.7.Sp.C.7

Find the probability of picking an even number between 1 and 10 (1 and 10 are included).

Explanation:

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

Now, given the event of picking an even number between 1 and 10, we can determine the following.

because there are 5 even numbers between 1 and 10:

• 2
• 4
• 6
• 8
• 10

Now, we can also determine the following:

because there are 10 different numbers we could potentially pick:

• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10

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

Therefore, the probability of picking an even number between 1 and 10 is .

### Example Question #111 : Statistics & Probability

Find the probability of drawing an Ace from a deck of cards.

Explanation:

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

Now, given the event of drawing an Ace from a deck of cards, we can calculate the following.

because there are 4 Aces in a deck of cards that we could draw:

• Ace of Hearts
• Ace of Diamonds
• Ace of Clubs

Now, we can calculate he following.

because there are 52 total cards within a deck that we could potentially draw.

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

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

### Example Question #51 : Develop And Compare Probability Models And Find Probabilities Of Events: Ccss.Math.Content.7.Sp.C.7

A bag contains the following:

• 3 blue pens
• 2 red pens
• 5 black pens
• 2 pencils

Find the probability of grabbing a pencil out of the bag.

Explanation:

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

Now, given the event of drawing a pencil out of the bag, we can determine the following:

because there are 2 pencils in the bag.

Now, we can determine the following:

because there are 12 total objects in the bag we could potentially draw:

• 3 blue pens
• 2 red pens
• 5 black pens
• 2 pencils

Now, knowing this, we can substitute into the formula.  We get

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

### Example Question #52 : Develop And Compare Probability Models And Find Probabilities Of Events: Ccss.Math.Content.7.Sp.C.7

A classroom contains 8 boys and 12 girls.

Find the probability the teacher calls on a boy.

Explanation:

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

Now, given the event of the teacher calling on a boy, we can determine the following:

because there are 8 boys in the classroom.

Now, we can determine the following:

because there are 20 total students in the class the teacher could potentially call on:

• 8 boys
• 12 girls

Now, knowing this, we can substitute into the formula.  We get

Therefore, the probability of the teacher calling on a boy is .

### Example Question #41 : Probability

A bag contains the following:

• 5 red pens
• 3 blue pens
• 4 black pens

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

Explanation:

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

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

because there are 3 blue pens in the bag.

Now, we can calculate the following:

because there are 12 pens in the bag we could potentially grab:

• 5 red pens
• 3 blue pens
• 4 black pens

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

Therefore, the probability of grabbing a blue pen from the bag is .