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

Now, given the event of grabbing a shirt from the closet, we can calculate the following:

because there are 10 shirts in the closet.

We can also calculate the following:

because there are 15 total things in the closet we could potentially grab:

•          10 shirts
•          2 jackets
•          3 pairs of jeans

Now, we can substitute.  We get

Therefore, the probability of grabbing a shirt from the closet is .

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

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

because there are 4 ways we can draw a 3 from a deck:

•          3 of clubs
•          3 of spades
•          3 of hearts
•          3 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 3 from a deck of cards is .

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

Now, given the event of a blue car leaves next, we can calculate the following:

\text{number of ways event can happen} = 7

because there are 7 blue cars in the lot

We can also calculate the following:

\text{total number of possible outcomes} = 11

because there are 11 total cars in the lot that could potentially leave:

•          7 blue cars
•          1 white car
•          3 black cars

Now, we can substitute. We get

Therefore, the probability that a blue car leaves the parking lot is .

The first thing you need to notice is that you need the probabilities for events opposite of those provided in your data.  Luckily, since there is a total of  for each discrete event, you know that there is a  it will not rain and a  chance that a philosopher will not say something strange.

Now, to calculate the chance of both these events occurring at the same time, you just need to multiply these two percentages together:

 or 

(You do not add them together, because you are talking about two independent events happening at the same time.)

In a small town, there is a  chance that person owns a pig and a  that a person owns a donkey.  What is the chance that a person owns at least one of these animals?

Based on our data, you can think of your information as meaning this:

• Has pig: 
• Doesn't have pig: 
• Has donkey: 
• Doesn't have donkey: 

Now, you are looking for cases of people owning both or just one.  Given that these are independent events, you calculate that probability by multiplying the numbers together.  Thus, you get:

• Pig and donkey: 
• Pig, no donkey: 
• Donkey, no pig: 

You could add these up and get:

 or 

Another way you could do this is by finding out the percentage that holds for NEITHER donkey NOR pig.  Then, you subtract this from .  This will give you the left over (namely, NOT NONE or in other words, AT LEAST ONE):

 or 

Subtracted from , that is still 

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

Given the event of drawing a black card from a deck of cards, we can calculate the following:

because there are 26 black cards in a deck

•          13 clubs
•          13 spades

Now, we can calculate the following:

because there are 52 total cards we could potentially draw.

So, we can substitute. We get

Therefore, the probability of drawing a black card from a deck of cards is .

For Bob, the desirable rolls would be 2, 5, 7, and 10, each of which would land him on a white space.

There are 36 ways to roll a pair of fair six-sided dice; the rolls are seen below, with the desirable rolls circled:

There are 14 desirable rolls out of 36 total, making the probability of rolling one of these

.

Examine the diagram below, which shows the possible rolls of two fair six-sided dice. As seen, there are six ways to roll doubles:

The probability that Julie will roll doubles in any given turn is 

,

so the probability she will not roll doubles in a given turn is 1 minus this, or

 .

Apply the multiplication principle to find the probability that she will go three turns without rolling doubles:

.

Therefore, the probability that Julie will roll doubles within three turns is 1 minus this, or

.

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

Now, given the event of a black car leaves next, we can calculate the following:

\text{number of ways event can happen} = 11

because there are 11 black cars in the lot.

We can also calculate the following:

\text{total number of possible outcomes} = 22

because there are 9 total cars in the lot that could potentially leave

• 11 black cars
• 8 red cars
• 3 blue cars

Now, we can substitute. We get

Therefore, the probability that a black car leaves the parking lot is .

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

Now, given the event of grabbing a marker, we can calculate the following:

because there is 1 marker we can grab.

We can also calculate the following:

because there are 7 objects we could potentially grab:

• 2 pencils
• 4 pens
• 1 marker

Now, we can substitute. We get

Therefore, the probability of grabbing a marker from the bag is .