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

Now, given the event of rolling a multiple of 3 on a dice, we can determine the following.

because there are 2 multiples of 3 on a dice:

• 3
• 6

Now, we can also determine the following:

because there are 6 different numbers we could potentially roll:

• 1
• 2
• 3
• 4
• 5
• 6

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

Therefore, the probability of rolling a multiple of 3 on a dice is 

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 .

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

Now, given the event of rolling a factor of 5, we can calculate the following.

because there are 2 factors of 5 on a dice:

• 1
• 5

We can also calculate the following.

because there are 6 different possible numbers we can roll on a dice:

• 1
• 2
• 3
• 4
• 5
• 6

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

Therefore, the probability of rolling a factor of 5 on a dice is .

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

Now, given the event of rolling a multiple of 2, we can calculate the following.

because there are 3 multiples of 2 on a dice:

• 2
• 4
• 6

We can also calculate the following.

because there are 6 different possible numbers we can roll on a dice:

• 1
• 2
• 3
• 4
• 5
• 6

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

Therefore, the probability of rolling a multiple of 2 on a dice is .

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 Spades
• 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 .

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

Now, given the event of rolling a factor of 2 on a dice, we can calculate the following.

because there are 2 factors of 2 on a dice:

• 1
• 2

Now, we can calculate he following.

because there are 6 possible numbers we could potentially roll on a dice:

• 1
• 2
• 3
• 4
• 5
• 6 

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

Therefore, the probability of rolling a factor of 2 on a dice is .

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 .

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 .

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 .

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

Now, given the event of rolling a factor of 6 on a dice, we can calculate the following:

because there are 4 factors of 6 on a dice:

• 1
• 2
• 3
• 6

Now, we can calculate the following:

because there are 6 possible outcomes we could potentially get when rolling a dice:

• 1
• 2
• 3
• 4
• 5
• 6

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

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