# The probability that both events E and F occur is 0.42

The probability that both events \$E\$ and \$F\$ occur is \$0.42\$.

 Quantity A \$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\$ Quantity B \$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\$ The probability that event \$E\$ will occur \$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\$ \$0.58\$
1. Quantity A is greater.
2. Quantity B is greater.
3. The two quantities are equal.
4. The relationship cannot be determined from the information given.

So, you were trying to be a good test taker and practice for the GRE with PowerPrep online. Buuuut then you had some questions about the quant section—specifically question 6 of Section 6 of Practice Test 1. Those questions testing our knowledge of Probability can be kind of tricky, but never fear, PrepScholar has got your back!

## Survey the Question

Let’s search the problem for clues as to what it will be testing, as this will help shift our minds to think about what type of math knowledge we’ll use to solve this question. Pay attention to any words that sound math-specific and anything special about what the numbers look like, and mark them on our paper.

Since the question asks for a probability, it probably tests our knowledge of the Probability math skill for the GRE. Let’s keep what we’ve learned about this skill at the tip of our minds as we approach this question.

## What Do We Know?

Let’s carefully read through the question and make a list of the things that we know.

1. We know the probability that both events \$E\$ and \$F\$ occur is \$0.42\$
2. We want to compare the probability of \$E\$ occurring to the value \$0.58\$

## Develop a Plan

We’re given a joint probability between two events, which is the probability that \$E\$ and \$F\$ both occur.
As an example, this is like telling us that the probability of us Eating enchiladas AND Feeding on fish this evening is \$0.42\$. This tells us that at a minimum the probability for each individual event here is \$0.42\$. After all, for the two events to happen together, each one of them MUST happen. However, this does not place an upper limit on the probability of a single event occurring here. For example, we could have a probability of Eating enchiladas of \$0.42\$ and a probability of Feeding on fish of \$1\$, and the probability of both events occurring would still be \$0.42\$. On the other hand, we could have a probability of Eating enchiladas of \$1\$ and a probability of Feeding on fish of \$0.42\$, and the probability of both events occurring would still be \$0.42\$. So in essence, we know that the probability for event \$E\$ is somewhere between \$0.42\$ and \$1\$, inclusive.

## Solve the Question

Well, we’ve determined that Quantity A must be between \$0.42\$ and \$1\$. This means that Quantity A could be less than \$0.58\$, equal to \$0.58\$, or even greater than \$0.58\$. We need more information to know for sure. So the correct answer is D, the relationship cannot be determined from the information given.

## What Did We Learn

We definitely needed to be careful here. The \$0.58\$ was a somewhat curious number, as we know that the probabilities for all possible events must sum up to \$1\$, and \$0.42+0.58=1\$. This just goes to show that it is important to read these questions carefully and not just rely on coincidental numerical relationships. Otherwise we’ll probably fall into a clever wrong answer trap on test day.

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