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 .

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 .

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 .

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 .