# 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.

$Probability = \frac{relevant}{whole} = \frac{BC}{AC} = \frac{3x}{5x} = \frac{3}{5}$

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