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Probability on the SAT: “Easy” Concept, Tricky Questions
Usually, students think they understand probability, but they inevitably miss probability questions on the SAT and ACT, particularly when those probability questions are word problems with a table attached. Why do they miss these questions? It’s simple. They fail to READ exactly what the question is asking for. Don’t make this mistake! Follow along as I guide you through a tricky SAT probability question and explain exactly how to handle it, as well as address some common mistakes and clear up what you need to know as far as probability’s concerned. Let’s get to it!
What is probability?
Probability refers to the likelihood of any given outcome. It can be expressed as a percentage chance or as a fraction. Let’s take a look at a basic probability question to see this concept in action.
Sally has a bag of 20 different-colored marbles. She has red marbles, blue marbles, and green marbles. If Sally has 5 red marbles, 7 blue marbles, and 8 green marbles, and if Sally decides to randomly select a marble from the bag, what is the probability that Sally would select a blue marble?
This question isn’t bad at all. You simply need to read what it’s asking for. Probability can be expressed as a fraction in the classic concept of part out of whole, as such:
Probability = the number of desirable outcomes over the number of possible outcomes
How does that concept work in this problem? It’s easy. How many desirable outcomes are there? Well, in this problem, the question wants Sally to select a blue marble, and so the number of desirable outcomes is equal to the number of blue marbles, i.e. 7. And what’s the number of possible outcomes? Well, Sally has 20 marbles to choose from. Therefore, the probability that Sally will select a blue marble is 7 out of 20, or 35%.
Make sure to READ the question
Imagine if the question above were worded slightly differently. What if the problem asked for the probability that Sally would select a marble that is NOT blue? The answer would be entirely different. Since there are 13 marbles that aren’t blue, the probability of not selecting a blue marble would be 13/20 or 65%. On a basic question like the one we just saw, this is pretty easy. But in the problem that follows, most students are simply too lazy or are in too big of a hurry to really read what the question wants. Let’s have a look!
Tricky SAT Probability Question
First of all, what makes this a tricky probability question? It isn’t that it requires a ton of math. It’s that it requires a basic understanding of probability and a willingness to read EXACTLY what the question wants.
What do you think the answer is?
Probability, remember, is always part over whole, or the number of desirable outcomes over the number of possible outcomes. But in this problem, they’re really messing with. They’re hoping that you fail to read the problem or interpret the table. In this question, the number of total outcomes is NOT 200, even though there were 200 total students surveyed.
The problem says that “a person is chosen from random from those who recalled at least one dream” and wants to know “what is the probability that the person belonged to group Y?”
So in this case, we’re not choosing from EVERYONE. We’re choosing from “those who recalled at least one dream.” And “at least one dream” doesn’t just mean 1-4. It means, in this table, everyone who recalled 1-4 dreams or 5 or more dreams. The total number of people who recalled at least one dream is therefore 39+125, which equals 164. The number of possible outcomes for this question is 164.
Now we want to know the probability that the person belonged to group Y. So we can’t simply look at EVERYONE who belonged to Group Y. We need to know the number of people from Group Y who recalled at least one dream. That number, according to the table, is 11+68, which equals 79.
Therefore, if we’re choosing from the 164 people who recalled at least one dream and there are 79 people from Group Y who recalled at least one dream, the probability of the scenario that the question outlines is 79 out of 164, or answer choice C.
Were you able to solve this problem? It’s not “hard” in the sense that it requires difficult math. It’s hard simply because people don’t read exactly what the problem wants or fail to correctly interpret the table!
Hopefully this problem helps to encourage you to gain a basic understanding of probability and to read the question and all associated figures very carefully!
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