There are   possible rolls of two fair six-sided dice, each of which will come up with equal probability. The set of rolls is shown below, with the ways to roll a sum of 8 or 9 indicated.

There are 9 ways out of 36 to roll a sum of 8 or 9, making the probability of this outcome .

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

So, if we look at the event of drawing a 10 from a deck of cards, we can determine the following:

because there are 4 ways we can draw a 10:

• 10 of hearts
• 10 of diamonds
• 10 of clubs
• 10 of spades

because there are 52 total cards to choose from.  

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

Now, we simplify.

Therefore, the probability of drawing a 10 from a deck of cards is .

The first step is to take the seniors out of the equation 

.  

With  students left over, you divide that number by three since each of the three remaining groups are equally likely.  

This gives you a final answer of .

Since there are  males at the concert, that means there are  women 

.  

To find the probability of selecting a woman, you divide the number of women by the total number of quests giving you 

.

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.