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

$\displaystyle \text{probability of event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$

So, given the event of drawing a 3 from a deck of cards, we can calculate the following:

$\displaystyle \text{number of ways event can happen} = 4$

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:

$\displaystyle \text{total number of possible outcomes} = 52$

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

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

$\displaystyle \text{probability of drawing a 3} = \frac{4}{52}$

$\displaystyle \text{probability of drawing a 3} = \frac{2}{26}$

$\displaystyle \text{probability of drawing a 3} = \frac{1}{13}$

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

$\displaystyle \text{probability of event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$

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

$\displaystyle \text{number of ways event can happen} = 4$

Because there are 4 green crayons in the bag.

We can also calculate the following:

$\displaystyle \text{total number of possible outcomes} = 24$

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

$\displaystyle \text{probability of grabbing a green crayon} = \frac{4}{24}$

$\displaystyle \text{probability of grabbing a green crayon} = \frac{2}{12}$

$\displaystyle \text{probability of grabbing a green crayon} = \frac{1}{6}$

Therefore, the probability of grabbing a green crayon is $\displaystyle \frac{1}{6}$.

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

$\displaystyle \text{probability of event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$

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

$\displaystyle \text{number of ways event can happen} = 24$

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

We can determine:

$\displaystyle \text{total number of possible outcomes} = 56$

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

• 24 girls
• 32 boys

$\displaystyle 24+32=56$

Now, we can substitute into the formula.  We get

$\displaystyle \text{probability of calling on a girl} = \frac{24}{56}$

$\displaystyle \text{probability of calling on a girl} = \frac{12}{28}$

$\displaystyle \text{probability of calling on a girl} = \frac{6}{14}$

$\displaystyle \text{probability of calling on a girl} = \frac{3}{7}$

Therefore, the probability the teacher calls on a girl is $\displaystyle \frac{3}{7}$.

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

$\displaystyle \text{probability of event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$

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

$\displaystyle \text{number of ways event can happen} = 4$

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:

$\displaystyle \text{total number of possible outcomes} = 52$

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

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

$\displaystyle \text{probability of drawing a 7} = \frac{4}{52}$

$\displaystyle \text{probability of drawing a 7} = \frac{2}{26}$

$\displaystyle \text{probability of drawing a 7} = \frac{1}{13}$

Therefore, the probability of drawing a 7 from a deck of cards is $\displaystyle \frac{1}{13}$.

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

$\displaystyle \text{probability of event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$

So, given the event of drawing heart, we can calculate the following:

$\displaystyle \text{number of ways event can happen} = 13$

because there are 13 ways we can draw a heart:

• Ace
• Two
• Three
• Four
• Five
• Six
• Seven
• Eight
• Nine
• Ten
• Jack
• Queen
• King

Now, we can calculate the following:

$\displaystyle \text{total number of possible outcomes} = 52$

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

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

$\displaystyle \text{probability of drawing a heart} = \frac{13}{52}$

$\displaystyle \text{probability of drawing a heart} = \frac{1}{4}$

Therefore, the probability of drawing a heart from a deck of cards is $\displaystyle \frac{1}{4}$.

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

$\displaystyle \text{probability of event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$

Now, given the event of grabbing a red crayon from the box, we can calculate:

$\displaystyle \text{number of ways event can happen} = 4$

because there are 4 red crayons in the box we could grab.

We can also calculate:

$\displaystyle \text{total number of possible outcomes} = 17$

because there are 17 total crayons we could potentially grab:

• 9 blue crayons
• 3 green crayons
• 4 red crayons
• 1 yellow crayon

$\displaystyle 9+3+4+1=17$

So, we get

$\displaystyle \text{probability of grabbing a red crayon} = \frac{4}{17}$

Therefore, the probability of grabbing a red crayon from the box is $\displaystyle \frac{4}{17}$.

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

$\displaystyle \text{probability of event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$

So, given the event of drawing a 5, we can calculate the following:

$\displaystyle \text{number of ways event can happen} = 4$

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

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

Now, we can calculate the following:

$\displaystyle \text{total number of possible outcomes} = 52$

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

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

$\displaystyle \text{probability of drawing a 5} = \frac{4}{52}$

$\displaystyle \text{probability of drawing a 5} = \frac{2}{26}$

$\displaystyle \text{probability of drawing a 5} = \frac{1}{13}$

Therefore, the probability of drawing a 5 from a deck of cards is $\displaystyle \frac{1}{13}$.

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

$\displaystyle \text{probability of an event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$

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

$\displaystyle \text{number of ways event can happen} = 10$

because there are 10 boy students in the class.

To find the number of possible outcomes, we get

$\displaystyle \text{total number of possible outcomes} = 22$

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

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

$\displaystyle \text{probability of calling on a boy} = \frac{10}{22}$

Reduce:

$\displaystyle \text{probability of calling on a boy} = \frac{5}{11}$

Therefore, the probability of calling on a boy is $\displaystyle \frac{5}{11}$.

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

The event outcomes would be the $\displaystyle 12$ seniors on the bus.  

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

$\displaystyle 42 \left ( 9+10+11+12=42\right )$.  

So the probability of picking a senior would be 

$\displaystyle \frac{12}{42}=0.29$.

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

$\displaystyle \text{probability of event} = \frac{\text{number of ways event can happen}}{\text{total number of possible events}}$

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

$\displaystyle \text{number of ways event can happen} = 4$

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,

$\displaystyle \text{total number of possible events} = 6$

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

$\displaystyle \text{probability of rolling a factor of 6} = \frac{4}{6}$

Now, we will simplify.  We get

$\displaystyle \text{probability of rolling a factor of 6} = \frac{2}{3}$

Therefore, the probability of rolling a factor of 6 is $\displaystyle \frac{2}{3}$.