SAT Probability Question 52 | Free SAT Prep | Aniko

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Question 52·Easy·Probability and Conditional Probability

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A bowl contains $x$ oatmeal cookies and 5 chocolate chip cookies. If one cookie is selected at random, what is the probability that the cookie chosen is an oatmeal cookie, in terms of $x$ ?

For SAT probability questions with a simple scenario (like picking an item from a group), immediately identify two numbers: the count of favorable outcomes (what you want) and the total number of possible outcomes. Write probability as a fraction favorable / total, being careful not to mix up which quantity goes in the numerator, and if variables are used, express both favorable and total in terms of those variables before simplifying. This quickly rules out choices that use the wrong total or swap numerator and denominator.

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Think about totals

How many cookies are in the bowl altogether if there are $x$ oatmeal cookies and 5 chocolate chip cookies?

Recall the basic probability formula

Probability of an event is the number of outcomes that match the event divided by the total number of possible outcomes.

Identify the favorable outcomes

In this problem, which cookies count as a "success" (favorable outcome) when one cookie is chosen at random, and how many of those are there?

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Pick a specific value for x

Choose a positive whole number for $x$ , such as $x = 10$ , meaning 10 oatmeal cookies and 5 chocolate chip cookies, for a total of 15 cookies.

Compute the actual probability numerically

In Desmos, type the fraction representing the situation for your chosen $x$ , for example 10/(10+5) if $x=10$ . This is the true probability of picking an oatmeal cookie for that value of $x$ .

Test each answer choice with the same x

In Desmos, enter each choice using your chosen $x$ value, such as 10/5, 10/(10+5), 5/10, and 5/(10+5). Compare each numerical result to the probability you computed in the previous step and see which expression matches it.

Step-by-step Explanation

Understand what probability means

Probability in this type of problem is

\text{Probability} = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}.

Here, a "favorable outcome" means choosing an oatmeal cookie.

Find the total number of cookies

The bowl has $x$ oatmeal cookies and 5 chocolate chip cookies.

Number of oatmeal cookies: $x$
Number of chocolate chip cookies: $5$

So the total number of cookies is

\text{total} = x + 5.

Write the probability as a fraction

The number of favorable outcomes (choosing an oatmeal cookie) is $x$ , and the total number of outcomes is $x+5$ .

So the probability of choosing an oatmeal cookie is

\frac{\text{favorable}}{\text{total}} = \frac{x}{x+5},

which corresponds to choice B.

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Step-by-step Explanation

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Step-by-step Explanation