Remember that the "probability" of an event happening is the number of outcomes which result in that event divided by the total number of possible outcomes. That is,

.

Hence, the probability of an event happening is described as a fraction. To solve this problem, we must first recognize that three separate events are being described: drawing an ace, drawing a king, and drawing a jack. Because each of these events do not overlap (you cannot, for example, draw a card that is both a jack and a king at the same time), calculating the probability  that you draw any one of them is a simple matter of adding together their respective probabilities , , and .

There are  cards in a deck of playing cards,  of which are aces,  of which are kings, and  of which are jacks. Hence, 

, 

, and

,

and therefore

This means that the probability of drawing either an ace, a king, or a jack from a standard deck of playing cards is .

Mrs. Smith assigns homework to her class once a week and records each student's results. For last week's assignment, the histogram depicts these results. If the homework set was worth twenty points, what is the range of grades for last week's assignment?

Note: For each error, one point is subtracted from the total points possible. 

To solve this problem, first identify what the highest and lowest grade on the assignment was. The highest grade will be the one with the least amount of errors made and the lowest grade will be the one with the most amount of errors made.

The red bar in the histogram says that students made between zero and two errors. In other words, either: 0, 1, 2 errors.

The yellow bar in the histogram says that the students made between two and four errors. Since the red bar includes two errors the yellow bar only includes 3 or 4 errors.

The green bar in the histogram says that students made 5 or 6 errors.

The teal bar in the histogram says that students made 7 or 8 errors.

The blue bar in the histogram says that students made 9 or 10 errors.

The purple bar in the histogram says that students made 11 or 12 errors.

This means that at least one student made zero errors on the assignment and therefore did not loose any points. Therefore, the highest grade on the assignment was twenty.

The histogram shows that at least one student made twelve errors on the test. Therefore, the lowest grade on the assignment would be:

From here, calculate the range.

When looking at the table

we can see that is shows several students and within the subjects of Math, Science, and Art what grades those students received in those classes.

So, going over the table briefly, we can see the first student Katrina.  We see for Math she received an A.  For science, Katrina received an A.  And for Art, Katrina got a B.  We can read the table similarly for the remaining students.

Now, the question asks how many students received an A in math.  So we will look through the table and locate Math.  Once we locate Math, we will look at the grade that corresponds with it (In this example, we do not care about who the student is.  We just care about the grade).  So, we will count the number of A's we see matched up to the subject Math.

Once we do that, we see there are 3 students who received A's in Math (Katrina, Chris, and Fionn).

Let's look at the table.

We can see the first column lists all the students.  The next column shows all of the classes.  And the last column shows the grade they received in those classes.

Now, to find which class Craig received the highest grade, we must first locate Craig.  We can see all of Craig's classes are at the very bottom of the table.

Now, we will look at the grade he got in each class by following along the rows with Craig's name.

We can see Craig's first class is Math.  He received a B.

Craig's second class is Science.  He received an A.

Craig's third class is Art.  He received a B.

Knowing this, we can see the highest grade Craig received was an A.  The class where he received an A was Science.

Therefore, the class that Craig received the highest grade was Science.

To answer the question, let's look at the table.

We can see the first column shows the different students, the next column shows the classes they are in, and the last column shows their grade in the class.

Now, to find what grade Chris received in Science, we will first locate Chris' name in the first column.

Now, we can see his name appears 3 times.  If we look to the right, we can see his name matches up to 3 different classes:  Math, Science, and Art.  We want to know his grade in Science, so we will choose that row.  

We will again look to the right to see the grade.  We can see that it says A.

Therefore, the grade that Chris received in Science was an A.

The given table reports the average high and low temperatures over four years. The question asks to calculate the average rate of change for the high temperature over the four years depicted.

To calculate average rate of change use the following formula.

Substitute these values into the formula looks as follows.

Therefore, the average rate of change for the high temperature from 2002 to 2005 is 2 degrees Fahrenheit.

The table reports the average high and low temperatures over four years. To calculate the fraction of average low temperatures in 2002 to 2005 first identify the average low temperature in 2002 and in 2005.

Examining the table,

Average low temperature in 2002: 34 degrees Fahrenheit.

Average low temperature in 2005: 45 degrees Fahrenheit.

From here, to find the fraction of average low temperatures during this time period, use the following formula.

To figure out which month had a higher approval rate, we need to divide the approve number by the total number of people.

From this, we can determine that October had the highest approval rate.

To determine what the rate is, we need to divide the proceeding value by the preceding value, for instance.

If we do this for the rest of the values, we will get the common ratio of .

In order to solve this, we need to look at the table. We simply take the number of men that played basketball and divide it by the total in the men row.