Since the first sock that Dave pulls out is black, there are 17 remaining socks in the drawer, 8 blue and 9 black. The probability that Dave will choose another black is sock is therefore 9 out of 17.

If Mark flips a coin, the chance that it will land on heads is . On a die, there are 2 out of 6 numbers that are a multiple of 3 (3 and 6); therefore, there is a  chance that the dice will be a multiple of 3. 

The probability that the coin will land on heads and that the dice will be a multiple of 3 is:

There are two possibilities every time you flip a coin and only one outcome. Therefore the probability for flipping either heads or tails each time is . When you have multiple trials in a row you multiply the probabilities of each outcome by each other. 

The number of balls in the box is 

.

The number of balls with even numbers is 

.

Therefore, if a ball is drawn at random, the probability that an even-numbered ball will be selected is

Each of the 26 letters is represented by one red ball; in addition, each of the five vowels is represented by two blue balls for a total of  blue balls. The total number of balls is

.

The probability that a random draw will result in a blue ball being selected 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; there will also be five unmarked yellow balls. The number of balls in the box will be , 5 of which are green, making the probability of a random draw resulting in a green ball

.

The number of balls in the box is 

;

The number of odd-numbered balls is 

.

Therefore, there are  balls that are not marked with an odd number, making the probability that one of these will be drawn .

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

Now, we will calculate the following:

because there are 4 different ways we can draw a 5 from a deck of cards:

• 5 of hearts
• 5 of diamonds
• 5 of spades
• 5 of clubs

Now, we will calculate the following:

because there are 52 different cards we could potentially draw from a deck. 

So, we will substitute.  We get

Therefore, the probability of drawing a 5 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 boy, we can calculate:

because there are 17 boys in the classroom who can be called on.

We can also calculate the following:

because there are 31 total students (14 girls + 17 boys = 31 students) who could potentially be called on.

Now, we can substitute.  We get

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

Wihtout the clubs, the deck comprises 39 cards, 26 of which are red.

The probability that the first card will be red will be . The probability that the second will then also be red will be . Multiply the probabilities, and result is