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

Now, we are asked to find the probability of drawing a 2 from a deck of cards.  Given that event, we can determine

because there are 4 ways to draw a 2 from a deck of cards:

• 2 of hearts
• 2 of diamonds
• 2 of clubs
• 2 of spades

Now, we can determine the total number of possible outcomes

because there are 52 different cards to choose from.

Knowing this, we can substitute into the formula.

Now, we can simplify.

Therefore, the probability of drawing a 2 from a deck of cards is .

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

Now, we are asked to find the probability of drawing an Ace of spades from a deck of cards.  Given that event, we can determine

because there is only 1 Ace of spades in a deck of cards.

Now, we can determine the total number of possible outcomes

because there are 52 different cards to choose from.

Knowing this, we can substitute into the formula.

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

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

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

because there are 4 Kings in a deck of cards:

1. King of Hearts
2. King of Diamonds
3. King of Clubs
4. King of Spades

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

Now, we simplify.

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

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 .