The number of balls in the box is 

$\displaystyle 1 + 2 + 3 + 4 + 5 +6 + 7 + 8 + 9 + 10 + 1 = 56$.

The number of even-numbered balls is

$\displaystyle 2+4+6+8+10 = 30$

leaving $\displaystyle 56-30 = 26$ balls without even numbers. This makes the probability of not drawing an even-numbered ball

$\displaystyle \frac{26}{56} = \frac{13}{28}$.

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 drawing an 8 from a deck of cards, we can calculate the number of ways the event can happen.  We get

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

because there are 4 different ways we can draw 8 from a deck of cards:

1. 8 of spades
2. 8 of clubs
3. 8 of hearts
4. 8 of diamonds

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

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

because there are 52 different cards we could possibly draw from a deck of cards.  Knowing this, we can substitute into the formula.  We get

$\displaystyle \text{probability of drawing an 8} = \frac{4}{52}$

Now, we can simplify.

$\displaystyle \text{probability of drawing an 8} = \frac{2}{26}$

$\displaystyle \text{probability of drawing an 8} = \frac{1}{13}$

Therefore, the probability of drawing an 8 from a deck of cards is $\displaystyle \frac{1}{13}$

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

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

Now, given the event of calling on a girl in the class, we can calculate the number of ways the event can happen.  We get

$\displaystyle \text{number of ways event can happen} = 14$

because there are 14 girls in the classroom.

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

$\displaystyle \text{total number of possible outcomes} = 26$

because there are 26 different students the teacher could possibly call on:

• 12 boys
• 14 girls

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

$\displaystyle \text{probability of calling on a girl} = \frac{14}{26}$

Now, we can simplify.

$\displaystyle \text{probability of calling on a girl} = \frac{7}{13}$

Therefore, the probability of calling on a girl in class is $\displaystyle \frac{7}{13}$

To find the probability of an event, we 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 diamond card from a deck of cards, we get

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

because there are 13 diamond cards in a deck of cards:

1. Ace of diamonds
2. Two of diamonds
3. Three of diamonds
4. Four of diamonds
5. Five of diamonds
6. Six of diamonds
7. Seven of diamonds
8. Eight of diamonds
9. Nine of diamonds
10. Ten of diamonds
11. Jack of diamonds
12. Queen of diamonds
13. King of diamonds

Now, we will find the total number of possible outcomes.  We get

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

because there are 52 cards to choose from within one deck.

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

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

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

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

To find the probability of an event, we 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 black card from a deck of cards, we get

$\displaystyle \text{number of ways event can happen} = 26$

because there are 26 black cards cards in a deck of cards:

• 13 cards that are Spades
• 13 cards that are Clubs

Now, we will find the total number of possible outcomes.  We get

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

because there are 52 cards to choose from within one deck.

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

$\displaystyle \text{probability of drawing a black card} = \frac{26}{52}$

$\displaystyle \text{probability of drawing a black card} = \frac{1}{2}$

Therefore, the probability of drawing a black card from a deck of cards is $\displaystyle \frac{1}{2}$.

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

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

Now, given the event of picking an even number between 1 and 10, we can determine the following.

$\displaystyle \text{number of ways event can happen} = 5$

because there are 5 even numbers between 1 and 10:

• 2
• 4
• 6
• 8
• 10

Now, we can also determine the following:

$\displaystyle \text{number of possible outcomes} = 10$

because there are 10 different numbers we could potentially pick:

• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10

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

$\displaystyle \text{probability of picking an even number between 1 and 10} = \frac{5}{10}$

$\displaystyle \text{probability of picking an even number between 1 and 10} = \frac{1}{2}$

Therefore, the probability of picking an even number between 1 and 10 is $\displaystyle \frac{1}{2}$.

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 drawing an Ace from a deck of cards, we can calculate the following.

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

because there are 4 Aces in a deck of cards that we could draw:

• Ace of Hearts
• Ace of Diamonds
• Ace of Spades
• Ace of Clubs

Now, we can calculate he following.

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

because there are 52 total cards within a deck that we could potentially draw. 

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

$\displaystyle \text{probability of drawing an Ace} = \frac{4}{52}$

$\displaystyle \text{probability of drawing an Ace} = \frac{2}{26}$

$\displaystyle \text{probability of drawing an Ace} = \frac{1}{13}$

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

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

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

Now, given the event of drawing a pencil out of the bag, we can determine the following:

$\displaystyle \text{number of ways event can happen} = 2$

because there are 2 pencils in the bag.

Now, we can determine the following:

$\displaystyle \text{total number of possible outcomes} = 12$

because there are 12 total objects in the bag we could potentially draw:

• 3 blue pens
• 2 red pens
• 5 black pens
• 2 pencils

$\displaystyle 3+2+5+2=12$

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

$\displaystyle \text{probability of drawing a pencil} = \frac{2}{12}$

$\displaystyle \text{probability of drawing a pencil} = \frac{1}{6}$

Therefore, the probability of drawing a pencil out of the bag 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 the teacher calling on a boy, we can determine the following:

$\displaystyle \text{number of ways event can happen} = 8$

because there are 8 boys in the classroom.

Now, we can determine the following:

$\displaystyle \text{total number of possible outcomes} = 20$

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

• 8 boys
• 12 girls

$\displaystyle 8+12=20$

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

$\displaystyle \text{probability of calling on a boy} = \frac{8}{20}$

$\displaystyle \text{probability of calling on a boy} = \frac{4}{10}$

$\displaystyle \text{probability of calling on a boy} = \frac{2}{5}$

Therefore, the probability of the teacher calling on a boy is $\displaystyle \frac{2}{5}$.

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 blue pen from the bag, we can calculate the following:

$\displaystyle \text{number of ways event can happen} = 3$

because there are 3 blue pens in the bag.

Now, we can calculate the following:

$\displaystyle \text{total number of possible outcomes} = 12$

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

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

$\displaystyle 5+3+4=12$

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

$\displaystyle \text{probability of grabbing a blue pen} = \frac{3}{12}$

$\displaystyle \text{probability of grabbing a blue pen} = \frac{1}{4}$

Therefore, the probability of grabbing a blue pen from the bag is $\displaystyle \frac{1}{4}$.