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

Now, in the event of calling on a boy in the class, we can determine the number of ways the event can happen:

because there are 10 boy students in the class.

To find the number of possible outcomes, we get

because there are 22 total students the teacher could potentially call on.

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

Therefore, the probability of calling on a boy is .

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

Now, in the event of calling on a girl in the class, we can determine the number of ways the event can happen:

because there are 12 girl students in the class.

To find the number of possible outcomes, we get

because there are 22 total students the teacher could potentially call on.

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

Therefore, the probability of calling on a girl is .

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

Now, given the event of drawing a green marble, we can calculate the following.

because there are 3 green marbles that we can pick.

Now, we can calculate the following.

because there are 6 total different marbles we could potentially pick.

Knowing this, we can substitute into the formula.

Therefore, the probability of picking a green marble from the box is .

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

Now, given the event of grabbing a bottle of water, we can calculate the following.

because there are 10 bottles of water we can grab.

Now, we can calculate the following.

because there are 18 total bottles in the refrigerator (10 water + 8 juice = 18 total).

Knowing this, we can substitute into the formula.

Therefore, the probability of picking a green marble from the box is .

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

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

because there are 10 girls in the classroom.

Now, we can calculate the following:

because there are 23 total students the teacher could potentially call on:

• 10 girls
• 13 boys

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:

Now, given the event of grabbing a black pen from the bag, we can calculate the following:

because there are 2 black pens in the bag.

Now, we can calculate the following:

because there are 7 objects in the bag we could potentially grab:

• 2 red pens
• 3 blue pens
• 2 black pens

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

Therefore, the probability of grabbing a black pen from the bag is .

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

So, given the event of drawing a black pen from a bag, we can calculate the following:

because there are 5 black pens in the bag we can choose from.

Now, we can calculate the following:

because there are 15 total objects in the bag we could potentially draw:

• 3 blue pens
• 5 black pens
• 7 red pens

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

Therefore, the probability of drawing a black pen from a bag is .

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

So, given the event of sitting in a red chair, we can calculate the following:

because there are 2 red chairs in the classroom.

Now, we can calculate the following:

because there are 15 different chairs we could potentially sit on.

• 6 black chairs
• 7 blue chairs
• 2 red chairs

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

Therefore, the probability of sitting in a red chair is .

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

Given the event of grabbing a blue pen from the bag, we can determine

because there are 5 blue pens in the bag. 

because there are 14 total pens in the bag we could potentially grab:

• 3 red pens
• 5 blue pens
• 6 black pens

Now, we can substitute into the formula.  We get

Therefore, the probability of grabbing a blue pen from the bag is .

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

So, given the event of grabbing a red pen from the bag, we can calculate:

because there is only 1 pen that we could grab from the bag.

We can also calculate the following:

because there are 6 pens we could potentially grab (2 blue + 3 black + 1 red = 6 pens). 

Now, we can substitute into the formula.  We get