Math / Data & Statistics

QuestionWhich of the following best describes the type of probability used in the scenario below?
A bag has 6 red marbles, 8 blue marbles, and 4 yellow marbles. The probability of drawing a blue at random is $\frac{4}{9}$ . A. Unpredictable B. Random C. Theoretical D. Empirical

Studdy Solution

STEP 1

What is this asking? We're figuring out if the probability given is based on theory or experiments! Watch out! Don't mix up theoretical and empirical probability; theoretical is what should happen, empirical is what did happen.

STEP 2

1. Analyze the given probability
2. Compare probability types

STEP 3

Alright, let's kick things off by finding the total number of marbles in the bag.
We've got $6$ red marbles, $8$ blue marbles, and $4$ yellow marbles.
So, the total is $6 + 8 + 4 = 18$ marbles.
Woohoo!

STEP 4

Now, let's see what the theoretical probability of grabbing a blue marble is.
We've got $8$ blue marbles out of a total of $18$ marbles.
So, the probability is $\frac{8}{18}$ .
Let's simplify that fraction by dividing both the numerator and denominator by their greatest common divisor, which is $2$ .
This gives us $\frac{8}{18} = \frac{8 \div 2}{18 \div 2} = \frac{4}{9}$ .
Boom!

STEP 5

Theoretical probability is all about what we expect to happen based on pure math, like calculating the odds of rolling a certain number on a die.
It's based on the possible outcomes and how likely each one is.

STEP 6

Empirical probability, on the other hand, is based on what actually happens when we do an experiment a bunch of times.
Like, if we flip a coin 100 times and get heads 55 times, the empirical probability of getting heads is $\frac{55}{100}$ .
It's all about real-world results!

STEP 7

The problem tells us the probability of drawing a blue marble is $\frac{4}{9}$ .
We calculated the theoretical probability of drawing a blue marble to also be $\frac{4}{9}$ .
They match!
This means the given probability is based on theory, not experiments.

STEP 8

The probability used in the scenario is theoretical, so the answer is C.

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QuestionWhich of the following best describes the type of probability used in the scenario below?
A bag has 6 red marbles, 8 blue marbles, and 4 yellow marbles. The probability of drawing a blue at random is $\frac{4}{9}$ . A. Unpredictable B. Random C. Theoretical D. Empirical

Studdy Solution

STEP 1

What is this asking? We're figuring out if the probability given is based on theory or experiments! Watch out! Don't mix up theoretical and empirical probability; theoretical is what should happen, empirical is what did happen.

STEP 2

1. Analyze the given probability
2. Compare probability types

STEP 3

Alright, let's kick things off by finding the total number of marbles in the bag.
We've got $6$ red marbles, $8$ blue marbles, and $4$ yellow marbles.
So, the total is $6 + 8 + 4 = 18$ marbles.
Woohoo!

STEP 4

STEP 5

Theoretical probability is all about what we expect to happen based on pure math, like calculating the odds of rolling a certain number on a die.
It's based on the possible outcomes and how likely each one is.

STEP 6

Empirical probability, on the other hand, is based on what actually happens when we do an experiment a bunch of times.
Like, if we flip a coin 100 times and get heads 55 times, the empirical probability of getting heads is $\frac{55}{100}$ .
It's all about real-world results!

STEP 7

The problem tells us the probability of drawing a blue marble is $\frac{4}{9}$ .
We calculated the theoretical probability of drawing a blue marble to also be $\frac{4}{9}$ .
They match!
This means the given probability is based on theory, not experiments.

STEP 8

The probability used in the scenario is theoretical, so the answer is C.

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QuestionWhich of the following best describes the type of probability used in the scenario below?A bag has 6 red marbles, 8 blue marbles, and 4 yellow marbles. The probability of drawing a blue at random is 49\frac{4}{9}94​. A. Unpredictable B. Random C. Theoretical D. Empirical

Studdy Solution

STEP 1

What is this asking? We're figuring out if the probability given is based on theory or experiments! Watch out! Don't mix up theoretical and empirical probability; theoretical is what *should* happen, empirical is what *did* happen.

STEP 2

1. Analyze the given probability2. Compare probability types

STEP 3

Alright, let's kick things off by finding the total number of marbles in the bag.We've got 666 red marbles, 888 blue marbles, and 444 yellow marbles.So, the **total** is 6+8+4=186 + 8 + 4 = 186+8+4=18 marbles.Woohoo!

STEP 4

STEP 5

Theoretical probability is all about what we *expect* to happen based on pure math, like calculating the odds of rolling a certain number on a die.It's based on the possible outcomes and how likely each one is.

STEP 6

Empirical probability, on the other hand, is based on what *actually* happens when we do an experiment a bunch of times.Like, if we flip a coin 100 times and get heads 55 times, the empirical probability of getting heads is 55100\frac{55}{100}10055​.It's all about real-world results!

STEP 7

The problem tells us the probability of drawing a blue marble is 49\frac{4}{9}94​.We calculated the *theoretical* probability of drawing a blue marble to *also* be 49\frac{4}{9}94​.They match!This means the given probability is based on theory, not experiments.

STEP 8

The probability used in the scenario is **theoretical**, so the answer is C.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWhich of the following best describes the type of probability used in the scenario below?
A bag has 6 red marbles, 8 blue marbles, and 4 yellow marbles. The probability of drawing a blue at random is $\frac{4}{9}$ . A. Unpredictable B. Random C. Theoretical D. Empirical

What is this asking? We're figuring out if the probability given is based on theory or experiments! Watch out! Don't mix up theoretical and empirical probability; theoretical is what should happen, empirical is what did happen.

1. Analyze the given probability
2. Compare probability types

Alright, let's kick things off by finding the total number of marbles in the bag.
We've got $6$ red marbles, $8$ blue marbles, and $4$ yellow marbles.
So, the total is $6 + 8 + 4 = 18$ marbles.
Woohoo!

Theoretical probability is all about what we expect to happen based on pure math, like calculating the odds of rolling a certain number on a die.
It's based on the possible outcomes and how likely each one is.

Empirical probability, on the other hand, is based on what actually happens when we do an experiment a bunch of times.
Like, if we flip a coin 100 times and get heads 55 times, the empirical probability of getting heads is $\frac{55}{100}$ .
It's all about real-world results!

The problem tells us the probability of drawing a blue marble is $\frac{4}{9}$ .
We calculated the theoretical probability of drawing a blue marble to also be $\frac{4}{9}$ .
They match!
This means the given probability is based on theory, not experiments.

The probability used in the scenario is theoretical, so the answer is C.