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Math  /  Data & Statistics

QuestionCalculate the relative frequency P(E)P(E) using the given information. P(E)=□P(E)=\square

Studdy Solution

STEP 1

What is this asking? We're finding the proportion of times an event EE happened out of all the trials, given the total number of trials and how many times EE happened. Watch out! Don't mix up the number of times EE happened with the *relative* frequency, which is a percentage or proportion.

STEP 2

1. Define relative frequency
2. Calculate the relative frequency

STEP 3

Alright, let's break this down! **Relative frequency**, often denoted as P(E)P(E), tells us how often an event EE occurs compared to the total number of trials.
It's like figuring out what percentage of a pizza you ate!

STEP 4

The formula for relative frequency is super straightforward: P(E)=fr(E)NP(E) = \frac{fr(E)}{N} Where fr(E)fr(E) is the **frequency** of event EE (how many times it happened), and NN is the **total number of trials** (like the total number of slices in the pizza).

STEP 5

We're given that fr(E)=200fr(E) = \textbf{200} and N=400N = \textbf{400}.
Let's plug those **values** into our **formula**: P(E)=200400P(E) = \frac{200}{400}

STEP 6

Now, we **simplify** the fraction by dividing both the **numerator** and the **denominator** by their **greatest common divisor**, which is 200.
Dividing the numerator by 200 gives us 1, and dividing the denominator by 200 gives us 2. P(E)=200400=200⋅1200⋅2=12P(E) = \frac{200}{400} = \frac{200 \cdot 1}{200 \cdot 2} = \frac{1}{2}

STEP 7

We can also express this as a decimal by dividing 1 by 2, which gives us **0.5**.
Or, if we multiply this decimal by 100, we get **50%**.
So, event EE occurred 50% of the time!

STEP 8

P(E)=12=0.5=50%P(E) = \frac{1}{2} = 0.5 = 50\%

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