# ISEE Middle Level Math : Probability

## Example Questions

### Example Question #41 : Probability

A large box contains some balls, each marked with a whole number from "1" to "10". Each number is represented by one red ball. In addition, each prime number is represented by one green ball, and each composite number is represented by one blue ball.

Give the probability that a randomly-drawn ball will be green.

Explanation:

Each number will be represented by one red ball, so there will be ten red balls in the box.

The prime numbers - the numbers that have only 1 and themselves as factors - are 2, 3, 5, and 7, so there will be four green balls.

The composite numbers - the numbers that have more than two factors - are 4, 6, 8, 9, and 10, so there will be five blue balls.

Note that 1 is neither prime nor composite.

The total number of balls is , four of which are green, so the probability of drawing a green ball at random is .

### Example Question #41 : How To Find The Probability Of An Outcome

A large box contains some balls, each marked with a whole number from "1" to "10". Each odd number is represented by one ball, which is red; each even number is represented by two balls, one red and one green.

Give the probability that a randomly-drawn ball will be red.

Explanation:

Each whole number from one to ten will be represented by a red ball, for a total of ten balls; each even number will be represented by a green ball, for a total of five balls. Therefore, ten out of fifteen, or

of the balls will be red, making this the probability that a red ball will be drawn.

### Example Question #42 : 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 #41 : How To Find The Probability Of An Outcome

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 #42 : How To Find The Probability Of An Outcome

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 #43 : How To Find The Probability Of An Outcome

Find the probability of rolling an odd number on a dice.

Explanation:

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

So, in the event of rolling an odd number on a dice, we can determine the number of times that event can happen.  So,

because there are 3 odd numbers on a dice:

• 1
• 3
• 5

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

because there are 6 different outcomes we can get when rolling the dice:

• 1
• 2
• 3
• 4
• 5
• 6

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

and we simplify.

Therefore, the probability of rolling an odd number on a dice is .

### Example Question #44 : How To Find The Probability Of An Outcome

Find the probability of rolling a factor of 4 on a dice.

Explanation:

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

So, in the event of rolling a factor of 4 on a dice, we can determine the number of times that event can happen.  So,

because there are 3 factors of 4 on a dice:

• 1
• 2
• 4

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

because there are 6 different outcomes we can get when rolling the dice:

• 1
• 2
• 3
• 4
• 5
• 6

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

and we simplify.

Therefore, the probability of rolling a factor of 4 on a dice is .

### Example Question #45 : How To Find The Probability Of An Outcome

Find the probability of rolling a factor of 6 on a dice.

Explanation:

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

Now, we will first determine the number of ways the event can happen. So, given the event of rolling a factor of 6, we get

because there are 4 different factors of 6 that we can roll:

• 1
• 2
• 3
• 6

Now, we will determine the total number of possible events.  So,

because there are 6 different numbers we can roll:

• 1
• 2
• 3
• 4
• 5
• 6

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

Now, we will simplify.  We get

Therefore, the probability of rolling a factor of 6 is .

### Example Question #46 : How To Find The Probability Of An Outcome

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 #41 : Outcomes

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 .