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 . 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:

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.

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.

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

The correct answer is (D).

On sat.collegeboard.org, 47% 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)

The correct answer is (C).


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

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

Probability

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

Read the question carefully, paying attention to the bottom line, the information that you must find.  Assess your options for solving the problem and attack the problem using the most efficient method possible.  In most cases you will not need to look at the answer choices until you have found your answer and double checked that it corresponds with your bottom line.

In the figure above, the length of  is 2x and the length of   is 3x.  If a point is chosen at random from , what is the probability that the point will lie on ?

Start by labeling the line with the information that you are given because it helps to have a visual.  Part of the line is 2x while part of the line is 3x.  Your bottom line is a probability, the likelihood of an event occurring.  Probability is expressed as the number of relevant outcomes divided by the total possible outcomes, so you will need to find the length of the whole line (your total).  

The total line length of the whole line from point A to C is: 2x + 3x = 5x.  

The point that is randomly chosen can be anywhere within the 5x length, so that number represents the whole.  The relevant part of the line is from point B to C (3x) because you are asked to find the probability that the point is between B and C.   When you plug in those numbers into the equation for probability, you have 3x divided by 5x.  Notice that you can simplify your answer because the variable cancels out.  Now look down at your answer choices.

  

(A) 

(B) 

(C) 

(D) 

(E) 

The correct answer is (C).

On sat.collegeboard.org, 69% of the responses were correct.

For more help with the writing section of the SAT, visit www.myknowsys.com!

Inequalities

Link of the Day

This page lists some of the great mathematicians of the ages, including Newton, Archimedes, Euclid, and others. Using any of them in an essay will help you stand out and earn a higher score. 

4/9 Inequalities

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

Be sure to read carefully--reading carelessly will cost you points. Mark the bottom line and assess your options, then choose the fastest route to the answer. Remember: The long way is the wrong way! After you find an answer, check it against your bottom line before looking among the answer choices for the number you found.

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 > -8?

First, look for your bottom line. It is in two parts here, so one thing you could do is try to combine them to simplify the problem. You could also find the numbers that satisfy each half of the bottom line and then combine them. The long way is the wrong way, so you will need to combine the inequalities. First, isolate x.

p (both inequalities) = ?

3x - 2 < 10                                                               x + 2 > -8

3x < 12                                                                    x > -10

x < 4

Next, you can combine the two inequalities into one compound inequality.

-10 < x < 4

Probability

Mathematics: Standard Multiple Choice

Read the following SAT Question and then select your answer. 

Remember to take the time to read carefully, to note the bottom line, to choose the fastest way to solve the problem, and to match your solution to the answer choices.

Of 5 employees, 3 are to be assigned an office and 2 are to be assigned a cubicle. If 3 of the employees are men and 2 are women, and if those assigned to the office are to be chosen at random, what is the probability that the offices will be assigned to 2 of the men and 1 of the women?

First, read carefully. There is a trap lurking here; it is easy to assume that the 3 men will get the offices and the 2 women will get cubicles just because the numbers match up. However, the question says that the offices are assigned randomly, not based on gender, so you will need a more sophisticated way to solve the problem. What is the bottom line? The question asks for "the probability that the offices will be assigned to 2 of the men and 1 of the women," so abbreviate that and put it at the top of your scratch work.

prob m,m,w=?