Of the 750 participants in a professional meeting, 450 are female

Of the $750$ participants in a professional meeting, $450$ are female and $1/2$ of the female and $1/4$ of the male participants are less than thirty years old. If one of the participants will be randomly selected to receive a prize, what is the probability that the person selected will be less than thirty years old?

  1. $1/8$
  2. $1/3$
  3. $3/8$
  4. $2/5$
  5. $3/4$

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 13 of Section 4 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 your paper.

The question asks for the probability of something happening, so it probably tests what we learned from the Probability data analysis math skill. So let’s keep in mind what we’ve learned about this skill 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. There are $750$ total people
  2. $450$ are females, the rest are males
  3. $1/2$ of the females are less than thirty years old
  4. $1/4$ of the males are less than thirty years old
  5. We want to know the probability of a randomly selected person being less than thirty years old

 

Develop a Plan

Let’s start with a top-down approach, where we will begin with what we’re looking for and work down to the details of what we’re given in this question. We want to know the probability of selecting a person who is less than thirty years old. We know the equation for probability is:

$$\Probability = {\Number \of \Successful \Possibilities}/{\Total \Number \of \Possibilities}$$

Since we want to know the probability of selecting a person less than thirty years old when randomly choosing from all of the people, we can define the probability as:

$$\Probability = {\Number \of \People \Less \Than \Thirty \Years \Old}/{\Total \Number \of \People}$$

We know that if we have the number of females less than thirty years old and the number of males less than thirty years old, we can add the two together to find the total number of people less than thirty years old:

$$\Number \of \People \Less \Than \Thirty \Years \Old = \Females \Less \Than \Thirty \Years \Old + \Males \Less \Than \Thirty \Years \Old$$

We know that $1/2$ of the females are less than thirty years old, so if we multiply $1/2$ by the number of females, we’ll get the number of females who less than thirty years old.

$$\;\;\;\;\;\,\Females \Less \Than \Thirty \Years \Old = 1/2 · 450$$
$$\Females \Less \Than \Thirty \Years \Old = 225$$

Since there are $750$ total people and $450$ of them are female, we know that the number of males is $750-450=300$. Next, we know that the number of males who are less than thirty years old will be the fraction of males that are less than thirty years old multiplied by the total number of males.

$$\;\;\;\;\;\;\;\;\Males \Less \Than \Thirty \Years \Old = 1/4 · 300$$
$$\Males \Less \Than \Thirty \Years \Old = 75$$

Excellent. We can now find the total number of people who are less than thirty years old, then calculate the probability of randomly selecting a person who is less than thirty years old.

Solve the Question

Let’s start with our first probability equation then plug in the values that we found earlier, simplifying as we go along the way:

$\Probability$ $=$ ${\Number \of \Less \Than \Thirty \Years \Old}/{\Total \Number \of \People}$
$\Probability$ $=$ ${\Males \Less \Than \Thirty \Years \Old + \Females \Less \Than \Thirty \Years \Old}/{\Total \Number \of \People}$
$\Probability$ $=$ ${225+75}/750$
$\Probability$ $=$ $300/750$
$\Probability$ $=$ $2/5$

The correct answer is D, $2/5$.

What Did We Learn

Probabilities! They’re all about successes divided by the total number. This problem became much easier to manage once we broke it down into smaller bits. Divide and conquer is definitely a great solution strategy.

 

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