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

Reduce:

Therefore, the probability of calling on a boy is .

To find the probability of an event, you divide the possible outcomes of that event by total outcomes.  

The event outcomes would be the  seniors on the bus.  

The total outcomes is the number of students on the bus which is 

.  

So the probability of picking a senior would be 

.

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

Now, we will first determine the number of ways the event can happen. So, given the event of rolling a factor of 6, we get

because there are 4 different factors of 6 that we can roll:

• 1
• 2
• 3
• 6

Now, we will determine the total number of possible events.  So,

because there are 6 different numbers we can roll:

• 1
• 2
• 3
• 4
• 5
• 6

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

Now, we will simplify.  We get

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

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

So, in the event of rolling a factor of 4 on a dice, we can determine the number of times that event can happen.  So,

because there are 3 factors of 4 on a dice:

• 1
• 2
• 4

Now, we can determine the total number of possible outcomes.  We get

because there are 6 different outcomes we can get when rolling the dice:

• 1
• 2
• 3
• 4
• 5
• 6

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

and we simplify.

Therefore, the probability of rolling a factor of 4 on a dice is .

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

So, in the event of rolling an odd number on a dice, we can determine the number of times that event can happen.  So,

because there are 3 odd numbers on a dice:

• 1
• 3
• 5

Now, we can determine the total number of possible outcomes.  We get

because there are 6 different outcomes we can get when rolling the dice:

• 1
• 2
• 3
• 4
• 5
• 6

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

and we simplify.

Therefore, the probability of rolling an odd number on a dice is .

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

So, if we look at the event of rolling an even number on a dice, we can determine the following:

because there are 3 ways we can roll an even number on a dice:

• 2
• 4
• 6

because there are 6 possible numbers we can roll:

• 1
• 2
• 3
• 4
• 5
• 6 

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

Now, we simplify.

Therefore, the probability of rolling an even number on a dice is .

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

Now, given the event of rolling a multiple of 3 on a dice, we can determine the following.

because there are 2 multiples of 3 on a dice:

• 3
• 6

Now, we can also determine the following:

because there are 6 different numbers we could potentially roll:

• 1
• 2
• 3
• 4
• 5
• 6

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

Therefore, the probability of rolling a multiple of 3 on a dice is 

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

Now, given the event of rolling a factor of 5, we can calculate the following.

because there are 2 factors of 5 on a dice:

• 1
• 5

We can also calculate the following.

because there are 6 different possible numbers we can roll on 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 5 on a dice is .

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

Now, given the event of rolling a multiple of 2, we can calculate the following.

because there are 3 multiples of 2 on a dice:

• 2
• 4
• 6

We can also calculate the following.

because there are 6 different possible numbers we can roll on a dice:

• 1
• 2
• 3
• 4
• 5
• 6

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

Therefore, the probability of rolling a multiple of 2 on a dice is .

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

Now, given the event of rolling a factor of 2 on a dice, we can calculate the following.

because there are 2 factors of 2 on a dice:

• 1
• 2

Now, we can calculate he following.

because there are 6 possible numbers we could potentially roll on 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 2 on a dice is .