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!