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

Now, given the event of the teacher calling on a boy, we can determine the following:

because there are 8 boys in the classroom.

Now, we can determine the following:

because there are 20 total students in the class the teacher could potentially call on:

• 8 boys
• 12 girls

Now, knowing this, we can substitute into the formula.  We get

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

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

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

because there are 3 blue pens in the bag.

Now, we can calculate the following:

because there are 12 pens in the bag we could potentially grab:

• 5 red pens
• 3 blue pens
• 4 black pens

Knowing this, 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:

Now, given the event of rolling a factor of 6 on a dice, we can calculate the following:

because there are 4 factors of 6 on a dice:

• 1
• 2
• 3
• 6

Now, we can calculate the following:

because there are 6 possible outcomes we could potentially get when rolling a dice:

• 1
• 2
• 3
• 4
• 5
• 6

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

Therefore, the probability of rolling a factor of 6 on a dice is .

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

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

Because there is only one 4 of Hearts in a deck of cards.

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 of Hearts 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 pencil from the bag, we can calculate the following:

Because there are 6 pencils in the bag.

Now, we can calculate the following:

Because there are 18 total items in the bag:

• 5 pens
• 6 pencils
• 7 markers

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

Therefore, the probability of drawing a pencil 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 the bag, we can calculate the following:

Because there are 15 black pens in the bag.

Now, we can calculate the following:

Because there are 30 total items in the bag to choose from:

• 10 red pens
• 15 black pens
• 5 blue pens

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

Therefore, the probability of drawing 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 3 from a deck of cards, we can calculate the following:

Beause there are four 3s we could draw from a deck of cards

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

Now we can calculate the following:

Because there are 52 cards in the deck we could potentially draw.

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

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

Now, given the event of grabbing  a green crayon from the bag, we can calculate the following:

Because there are 4 green crayons in the bag.

We can also calculate the following:

Because there are 24 total crayons we could potentially grab from the bag.

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

Therefore, the probability of grabbing a green crayon is .

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

Now, given the event of calling on a girl, we can determine:

because there are 24 girls in the class the teacher could call on.

We can determine:

because there are 56 total students in the class the teacher could potentially call on:

• 24 girls
• 32 boys

Now, we can substitute into the formula.  We get

Therefore, the probability the teacher calls on a girl is .

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

So, given the event of drawing a 7 from a deck of cards we can calculate the following:

because there are four ways we can draw a 7 from the deck: 

• 7 of clubs
• 7 of spades
• 7 of hearts
• 7 of diamonds

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 7 from a deck of cards is .