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

So, given the event of drawing a 7 of Diamonds from a deck of cards, we can see

because there is only 1 7 of Diamonds in a deck of cards.

Now, we will look at total outcomes.  We get

because there are 52 cards in a deck (in other words 52 different possibilities when drawing a card).

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

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

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 .

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.

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:

1. 8 of spades
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 

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 

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 .

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 .

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 .