The probability is expressed as the circumstance out of the whole number available.

The number of marbles that are red is 7, and the whole number of marbles is 20.

Therefore the probability is 

.

To find the probability of an event happening, we use the following

So, if we look at the number of ways we can draw a Queen, we can come up with

• Queen of Hearts
• Queen of Diamonds
• Queen of Spades
• Queen of Clubs

So, the number of ways we can draw a queen is equal to 4.  So,

Now, to find the total number of possible outcomes, we will think of how many different cards there are within a deck.  We know there are 52 total cards, which means there are 52 total possible outcomes.  So,

Now, we can simplify.

To find the probability of an event happening, we use the following

To calculate the number of ways this can happen it is important to recall that each suit (Hearts, Clubs, Spades, and Diamonds) have one value for numbers 1 through 10, one jack, one queen, one queen, and one ace. Therefore there is only one card that is the 2 of Hearts.

So, the number of ways we can draw a 2 of Hearts is equal to 1.  So,

Now, to find the total number of possible outcomes, we will think of how many different cards there are within a deck.  We know there are 52 total cards, which means there are 52 total possible outcomes.  So,

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

So, given the event of drawing a 4, we can calculate the following:

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

• 4 of Hearts
• 4 of Diamonds
• 4 of Clubs
• 4 of Spades

Now, we can calculate the following:

Because there are 52 cards we could potentially draw from a deck of cards.

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

Therefore, the probability of drawing a 4 from a deck of cards is .

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

So, given the event of the teacher calling on a girl, we can calculate the following:

Because there are 11 girls in the classroom.

Now, we can calculate the following:

Because there are 26 total students the teacher could potentially call on.

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

Therefore, the probability of the teacher calling on a girl is .

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

So, given the event of drawing a 3, we can calculate the following:

\text{number of ways event can happen} = 4

Because there are 4 ways we can draw a 3 from the deck:

• 3 of clubs
• 3 of spades
• 3 of diamonds
• 3 of hearts

Now, we can calculate the following:

 \text{total number of possible outcomes} = 52

Because there are 52 cards we could potentially draw from a deck of cards.

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

Therefore, the probability of drawing a 3 from a deck of cards is .