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Probability Posts

Multiple Choice on the SAT: How to Use the Answer Choices

Contrary to what you may think, the answer choices on the SAT are not designed to trap or trick you! We may describe them as “tricky” or “tempting” but seeing the answer choices can actually be a huge asset on Test Day. After all, we know that 1 of the 5 must be correct! Unlike grid-ins, we can often utilize the answer choices in problem solving questions to help us find the solution and get better SAT scores overall. Here are 5 ways you can make the answer choices work for you on your SAT Test!

For Writing question, remember that “No Error” is a strong option. For Identifying Sentence Error test questions, parts of a sentence are underlined. For this SAT question, Choice (E) is “No Error.” There is not always going to be an error. In fact, about 1/4th of the time, “No Error” is correct! Trust your instincts. If a sentence “sounds” okay, and you’ve checked the other four choices and found no grammatical mistake, the SAT alternative is choice E.

Eliminate (-) or (+) choices in Sentence Completions using your prediction. On test day, don’t simply read the sentence and plug in the answer choices, re-reading the SAT sentence five times. Identify the keywords that relate to the blank and write in your OWN word for the blanks, or at least predict whether the blank is a (+) or (-) word. Ace these tricky SAT questions by then eliminating answer choices that contain words with the opposite word charge!

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Elementary Probability

Probability questions on the SAT basically test if you know one concept – the definition of probability.

Probability = Number of times a certain event might occur/Total number of events that might occur

So if a question tells you that there are 120 dorm rooms and 24 of them are painted yellow, the probability that a freshman is placed in a yellow dorm room is 24/120 = 1/5 because there are 24 yellow rooms that the freshman could be placed in, out of a total of 120 rooms.

Reverse probability

To make things difficult, the question might ask you a reverse probability question.  For example, if there are 120 dorm rooms and Amy has a  chance of 1/6 being placed in a blue room, then how many blue rooms are there?  Using the formula above, if there is a one in six chance of getting a blue room, that means that the number of blue rooms out of the total number of rooms is 1/6.  Since there are 120 rooms in total, then 1/6 = blue rooms / 120.  This works out to 20 blue rooms.

Probability of an event not happening

Another type of question is one like this.  Suppose there are only blue and red marbles in a bag.  Let the number of blue marbles be b and the number of red marbles be r. If the probability of drawing a blue marble is 5/7, what is the value of b/r?  The only number you have to work with is 5/7.  This number represents the odds of picking a blue marble, meaning that 5/7 = number of blue marbles / total number of marbles.  You can thus let there be 5 blue marbles and 7 marbles in total.  This means that there are 2 red marbles, so the value b/r is 5/2.

This type of question is essentially testing if you know how to find the probability of an event not happening.  If the probability of getting a blue marble is 5/7, that means that the probability of not getting a blue marble (i.e. getting a red marble) is 1 – 5/7 or 2/7.

Probability of multiple events

The most difficult type of probability question on the SAT generally involves 2 dice.  Remember the question tells you that Joe rolls a pair of dice and forms a fraction x/y where x represents the number rolled on the first die and y represents the number rolled on the second die?  It then asks for the probability that this fraction equals 1.  To work out this problem, you need to know the total number of dice rolls that could occur.  Each dice can roll 6 different numbers, which means that with 2 dice, there are 6 x 6 = 36 possible combinations.  Of those 36 combinations, there are 6 ways of forming a fraction that equals 1.  If a 1 and 1, or a 2 and 2, or a 3 and 3, or a 4 and 4, or a 5 and 5 or a 6 and 6 is rolled.  In each of these cases, the fraction will equal 1.

So since there are 6 cases that give us the value we need, out of a possible 36, the probability is 6/36 = 1/6

Don’t forget that the probability of an event can never exceed 1.  If the probability of an event is 1, that means that it is certain to happen.  If the probability of an event is 0, that means that there is no chance of it ever happening.  Probability values never go higher than 1 or lower than 0, so if you find yourself with such an answer, double check to see what went wrong.

Check out Grockit for more probability practice!