# Probability

## Data Analysis: Probability

Read the following SAT test question and then select the correct answer.

Always read each question carefully and make a note of the bottom line (what you are trying to find).  Assess your options to find the best strategic method and use that method to attack the problem.  When you have an answer, loop back to verify that the answer matches the bottom line.

A jar contains only red marbles and green marbles. If a marble is selected at random from the jar, the probability that a red marble will be selected is $\frac{2}{3}$. If there are 36  green marbles in the jar, how many red marbles are there in the jar?

Bottom Line:  You want to know how many red marbles there are, so use r to represent red and just write r = ?

Assess your Options:  You could try to work backwards from the answer choices to find a number that, when combined with 36, makes the right fraction.  That won’t be any faster than just solving the problem.  Use the probability formula.

Attack the Problem:  The probability formula is:

$\frac{relevant\: outcomes}{total\: outcomes}$

In this problem, you know the red marbles are the relevant outcome, while the red and green marbles together are the total (all that is in the jar).  Use g for the green marbles.  There are 36 green marbles.

$\frac{r}{g + r}=\frac{r}{36+r}$

You have already been given the probability that a red marble will be selected.  Set the formula that you created equal to the probability that you were given.  Then solve for r with cross-multiplication.

$\frac{r}{36+r}=\frac{2}{3}$
3r = 2(36 + r)
3r = 72 + 2r
r = 72

Loop Back:  You solved for your bottom line, so you are ready to look at the answer choices.

(A) 18
(B) 24
(C) 54
(D) 72
(E) 108

On sat.collegeboard.org, 47% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!

# Scatterplots

## Data Analysis: Scatterplots

Read the following SAT test question and then select the correct answer.

Always read the question carefully so that you can glean as much information from it as possible.  Identify the bottom line – what is it asking?  Then assess your options and choose the most efficient method to attack the problem.  When you have a solution, loop back to make sure that it matches your bottom line.

The scatterplot above shows the number of items purchased at a grocery store by 28 customers and the total cost of each purchase. How many of these 28 customers bought more than 10 items and spent less than $20? Bottom Line: # of people. Notice that this number must reflect those that meet 2 requirements: buying more than 10 things and spending less than$20.

Assess your Options:  When you have a graph, use the graph!  You can draw directly on it to help you visualize what you need.

Attack the Problem:  The dots represent each person.  Start with the first restriction.  If people must buy more than 10 items, then only the dots to the right of the 10 on the horizontal axis will be counted; those on the line do not count because they are equal to 10 rather than more than 10.  Draw a vertical line on the 10.  Now look at the second restriction.  If the people must spend less than $20, then they must be under the$20 hash mark on the vertical axis.  Draw a line at \$20.  Your graph should look like this:

Count the number of dots in the lower right hand region that you created.  Your answer is 4.

Loop Back:  Each dot represents a customer, a person, so you reached your bottom line.  Look down at your answer choices.

(A) Four
(B) Five
(C) Six
(D) Seven
(E) Eight

On sat.collegeboard.org, 66% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!

# Probability

## Data Analysis: Probability

Read the following SAT test question and then select the correct answer.

Read each question carefully to avoid making any mistakes. Identify the bottom line (what the question is asking) and assess your options for reaching it by asking yourself “What could I do?” and “What should I do?” Choose the most efficient method to attack the problem and find an answer. Last, loop back to make sure that your answer addresses the bottom line.

If a number is chosen at random from the set {-10, -5, 0, 5, 10}, what is the probability that it is a member of the solution set of both 3x – 2 <10 and x + 2?

Bottom Line: Prb = ?

Assess Your Options: You cannot solve for a probability until you know whether each number in the set meets the requirements that you are given. You could plug numbers from the set into each inequality and see if they work, but it is much faster to simplify the inequalities before you begin working with them.

Attack the Problem: Simplify the inequalities by solving both for x.

3x – 2 < 10
3x < 12
x < 4

x + 2 > -8
x > -10

You now know that x must be less than 4, but greater than -10. The question asked you to find a number that fits both of these solution sets. Look at the original set that you were given. The only two answers that are between -10 and 4 are -5 and 0 (-10 does not work because it cannot be equal to negative -10; it has to be greater than -10). You found 2 numbers out of 5 that you were given that work. To write this as a probability, you must set the number of relevant outcomes over the number of total possible outcomes. Your answer is .

Loop Back: You found a probability matching the restrictions you were given. Look down at your answer choices.

(A) 0

(B)

(C)

(D)

(E)

On sat.collegeboard.org, 50% of the responses were correct.

For more help with SAT math, visitwww.myknowsys.com!

# Circle Graph

Read the following SAT test question and then select the correct answer.

When a math question involves a table or chart, read both the text of the question and the labels of the chart carefully.  Identify the bottom line, and assess your options for solving the problem.  Attack the problem to find the answer, and loop back to make sure that your answer addresses the bottom line.

In a survey, a group of students from Westville High School were asked about their favorite movie genre. Each student in the group selected exactly one movie genre, and the data collected are summarized in the circle graph above. If 40 more students chose Action than Fiction, how many students were surveyed in total?

Bottom Line:  Total students = ?

Assess your Options:  You could plug in answer choices for the total and then take percentages of those to find out which answer would produce a difference of 40 between Action and Fiction.  That would take a lot of steps!  Instead, start with what you know and use what you know to write an equation.

Attack the Problem:  You know that 40 more students chose Action than Fiction.  That means that Action – Fiction = 40.  You also know the percentages for both Action and Fiction.  Plug in the percentage from the chart and you will see that 30% (Action) – 14% (Fiction) = 16%.  Now you need to combine the two things that you know, percents and actual numbers, into a single equation.  You can write percents as decimals by moving the decimal two times to the left.  What are these percents of?  The uknown total number of students.  For any unknown number, you can plug in the variable x.  Now you have the equation .16x = 40.  Solve for x by dividing each side by .16 and you will get the answer 250.

Loop Back:  What did x represent?  The total number of students.  That matches your bottom line, so you are ready to look down at your answer choices.

(A) 100
(B) 150
(C) 200
(D) 250
(E) 300