Math / Data & Statistics

QuestionUse the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms.
Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. If the pointer lands on a borderline, spin again. Find the probability that the arrow will land on 2 or 3. A) 2 B) 1 C) $\frac{2}{5}$ D) $\frac{3}{2}$

Studdy Solution

STEP 1

What is this asking? What are the chances of landing on a 2 or a 3 on this spinner with five equal sections? Watch out! Don't mix up "or" (meaning one or the other or both) with "and" (meaning both must happen at the same time).
Also, make sure to simplify that fraction!

STEP 2

1. Find the total number of possible outcomes.
2. Find the number of favorable outcomes.
3. Calculate the probability.

STEP 3

The spinner has five equally likely sections.
So, there are five possible outcomes: landing on 1, 2, 3, 4, or 5.
Let's call this $\text{Total Outcomes}$ .
So, $\text{Total Outcomes} = 5$ .

STEP 4

We want the pointer to land on 2 or 3.
That's two favorable outcomes.
Let's call this $\text{Favorable Outcomes}$ .
So, $\text{Favorable Outcomes} = 2$ .

STEP 5

Remember, probability is calculated as: $\text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}$

STEP 6

We know $\text{Favorable Outcomes} = 2$ and $\text{Total Outcomes} = 5$ .
Let's plug those values into our formula: $\text{Probability} = \frac{2}{5}$

STEP 7

The fraction $\frac{2}{5}$ is already in its simplest form because 2 and 5 share no common factors other than 1.
We can't simplify it any further!

STEP 8

The probability of the spinner landing on 2 or 3 is $\frac{2}{5}$ , which corresponds to answer choice C.

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Studdy Solution

STEP 1

What is this asking? What are the chances of landing on a 2 or a 3 on this spinner with five equal sections? Watch out! Don't mix up "or" (meaning one or the other or both) with "and" (meaning both must happen at the same time).
Also, make sure to simplify that fraction!

STEP 2

1. Find the total number of possible outcomes.
2. Find the number of favorable outcomes.
3. Calculate the probability.

STEP 3

The spinner has five equally likely sections.
So, there are five possible outcomes: landing on 1, 2, 3, 4, or 5.
Let's call this $\text{Total Outcomes}$ .
So, $\text{Total Outcomes} = 5$ .

STEP 4

We want the pointer to land on 2 or 3.
That's two favorable outcomes.
Let's call this $\text{Favorable Outcomes}$ .
So, $\text{Favorable Outcomes} = 2$ .

STEP 5

Remember, probability is calculated as: $\text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}$

STEP 6

We know $\text{Favorable Outcomes} = 2$ and $\text{Total Outcomes} = 5$ .
Let's plug those values into our formula: $\text{Probability} = \frac{2}{5}$

STEP 7

The fraction $\frac{2}{5}$ is already in its simplest form because 2 and 5 share no common factors other than 1.
We can't simplify it any further!

STEP 8

The probability of the spinner landing on 2 or 3 is $\frac{2}{5}$ , which corresponds to answer choice C.

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Studdy Solution

STEP 1

What is this asking? What are the chances of landing on a 2 *or* a 3 on this spinner with five equal sections? Watch out! Don't mix up "or" (meaning one or the other or both) with "and" (meaning both must happen at the same time).Also, make sure to simplify that fraction!

STEP 2

1. Find the total number of possible outcomes.2. Find the number of favorable outcomes.3. Calculate the probability.

STEP 3

The spinner has five equally likely sections.So, there are **five** possible outcomes: landing on 1, 2, 3, 4, or 5.Let's call this Total Outcomes\text{Total Outcomes}Total Outcomes.So, Total Outcomes=5\text{Total Outcomes} = 5Total Outcomes=5.

STEP 4

We want the pointer to land on 2 *or* 3.That's **two** favorable outcomes.Let's call this Favorable Outcomes\text{Favorable Outcomes}Favorable Outcomes.So, Favorable Outcomes=2\text{Favorable Outcomes} = 2Favorable Outcomes=2.

STEP 5

Remember, probability is calculated as: Probability=Favorable OutcomesTotal Outcomes \text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} Probability=Total OutcomesFavorable Outcomes​

STEP 6

We know Favorable Outcomes=2\text{Favorable Outcomes} = 2Favorable Outcomes=2 and Total Outcomes=5\text{Total Outcomes} = 5Total Outcomes=5.Let's plug those values into our formula: Probability=25 \text{Probability} = \frac{2}{5} Probability=52​

STEP 7

The fraction 25\frac{2}{5}52​ is already in its simplest form because 2 and 5 share no common factors other than 1.We can't simplify it any further!

STEP 8

The probability of the spinner landing on 2 or 3 is 25\frac{2}{5}52​, which corresponds to answer choice C.

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

What is this asking? What are the chances of landing on a 2 or a 3 on this spinner with five equal sections? Watch out! Don't mix up "or" (meaning one or the other or both) with "and" (meaning both must happen at the same time).
Also, make sure to simplify that fraction!

1. Find the total number of possible outcomes.
2. Find the number of favorable outcomes.
3. Calculate the probability.

The spinner has five equally likely sections.
So, there are five possible outcomes: landing on 1, 2, 3, 4, or 5.
Let's call this $\text{Total Outcomes}$ .
So, $\text{Total Outcomes} = 5$ .

We want the pointer to land on 2 or 3.
That's two favorable outcomes.
Let's call this $\text{Favorable Outcomes}$ .
So, $\text{Favorable Outcomes} = 2$ .

Remember, probability is calculated as: $\text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}$

We know $\text{Favorable Outcomes} = 2$ and $\text{Total Outcomes} = 5$ .
Let's plug those values into our formula: $\text{Probability} = \frac{2}{5}$

The fraction $\frac{2}{5}$ is already in its simplest form because 2 and 5 share no common factors other than 1.
We can't simplify it any further!

The probability of the spinner landing on 2 or 3 is $\frac{2}{5}$ , which corresponds to answer choice C.