Math / Data & Statistics

Question4. [-/5 Points]
DETAILS MY NOTES
The following table shows the frequency of outcomes when two distinguishable coins were tossed 6,800 times and the uppermost faces were observed. HINT [See Example 2.] \begin{tabular}{|r|c|c|c|c|} \hline Outcome & HH & HT & TH & TT \\ \hline Frequency & 1,800 & 1,650 & 1,900 & 1,450 \\ \hline \end{tabular}
What is the relative frequency that the first coin lands with heads up? (Round your answer to four decimal places.) $\square$

Studdy Solution

STEP 1

What is this asking? Out of all the times we flipped two coins, what fraction of the time did the first coin show heads? Watch out! Don't accidentally calculate the chances of both coins being heads, or of any coin being heads.
We only care about the first one!

STEP 2

1. Find the total number of tosses.
2. Find the number of tosses where the first coin was heads.
3. Calculate the relative frequency.

STEP 3

We're given that the coins were tossed a total of $6,800$ times.
This is our total sample size.
Super important number!

STEP 4

Look at the table!
We're looking for the outcomes where the first coin is heads.
That's HH and HT.

STEP 5

The table tells us HH happened $1,800$ times and HT happened $1,650$ times.
Let's add those up!

STEP 6

$1,800 + 1,650 = 3,450$ So, the first coin was heads a whopping $3,450$ times!

STEP 7

Relative frequency just means: how often something happened divided by the total number of tries.
It's like figuring out your batting average!

STEP 8

We know the first coin was heads $3,450$ times (from the previous addition), and there were a total of $6,800$ tosses.
So, the relative frequency is: $\frac{3,450}{6,800}$

STEP 9

Let's simplify that fraction!
Both the numerator and denominator are divisible by $10$ , so we can divide both by $10$ to get: $\frac{345}{680}$ Now, we can see that both the numerator and denominator are divisible by $5$ , so let's divide both by $5$ : $\frac{69}{136}$ We can further divide both by $69$ to get: $\frac{1}{2}$ We can also divide to get the decimal representation: $\frac{3,450}{6,800} = 0.50735294...$

STEP 10

The problem asks us to round to four decimal places.
Looking at the fifth decimal place, which is $5$ or greater, we round up the fourth decimal place.
So, our final answer is $0.5074$ .

STEP 11

The relative frequency of the first coin landing heads up is $0.5074$ .

Was this helpful?

Studdy Solution

STEP 1

What is this asking? Out of all the times we flipped two coins, what fraction of the time did the first coin show heads? Watch out! Don't accidentally calculate the chances of both coins being heads, or of any coin being heads.
We only care about the first one!

STEP 2

1. Find the total number of tosses.
2. Find the number of tosses where the first coin was heads.
3. Calculate the relative frequency.

STEP 3

We're given that the coins were tossed a total of $6,800$ times.
This is our total sample size.
Super important number!

STEP 4

Look at the table!
We're looking for the outcomes where the first coin is heads.
That's HH and HT.

STEP 5

The table tells us HH happened $1,800$ times and HT happened $1,650$ times.
Let's add those up!

STEP 6

$1,800 + 1,650 = 3,450$ So, the first coin was heads a whopping $3,450$ times!

STEP 7

Relative frequency just means: how often something happened divided by the total number of tries.
It's like figuring out your batting average!

STEP 8

We know the first coin was heads $3,450$ times (from the previous addition), and there were a total of $6,800$ tosses.
So, the relative frequency is: $\frac{3,450}{6,800}$

STEP 9

STEP 10

The problem asks us to round to four decimal places.
Looking at the fifth decimal place, which is $5$ or greater, we round up the fourth decimal place.
So, our final answer is $0.5074$ .

STEP 11

The relative frequency of the first coin landing heads up is $0.5074$ .

Get Studdy

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.

Studdy Solution

STEP 1

What is this asking? Out of all the times we flipped two coins, what fraction of the time did the *first* coin show heads? Watch out! Don't accidentally calculate the chances of *both* coins being heads, or of *any* coin being heads.We only care about the first one!

STEP 2

1. Find the total number of tosses.2. Find the number of tosses where the first coin was heads.3. Calculate the relative frequency.

STEP 3

We're given that the coins were tossed a **total** of 6,8006,8006,800 times.This is our **total sample size**.Super important number!

STEP 4

Look at the table!We're looking for the outcomes where the *first* coin is heads.That's **HH** and **HT**.

STEP 5

The table tells us **HH** happened 1,8001,8001,800 times and **HT** happened 1,6501,6501,650 times.Let's add those up!

STEP 6

1,800+1,650=3,4501,800 + 1,650 = 3,4501,800+1,650=3,450 So, the first coin was heads a whopping 3,4503,4503,450 times!

STEP 7

**Relative frequency** just means: how often something happened divided by the total number of tries.It's like figuring out your batting average!

STEP 8

We know the first coin was heads 3,4503,4503,450 times (from the previous addition), and there were a total of 6,8006,8006,800 tosses.So, the relative frequency is: 3,4506,800\frac{3,450}{6,800}6,8003,450​

STEP 9

STEP 10

The problem asks us to round to four decimal places.Looking at the fifth decimal place, which is 555 or greater, we round up the fourth decimal place.So, our **final answer** is 0.50740.50740.5074.

STEP 11

The relative frequency of the first coin landing heads up is 0.50740.50740.5074.

Get Studdy

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.

What is this asking? Out of all the times we flipped two coins, what fraction of the time did the first coin show heads? Watch out! Don't accidentally calculate the chances of both coins being heads, or of any coin being heads.
We only care about the first one!

1. Find the total number of tosses.
2. Find the number of tosses where the first coin was heads.
3. Calculate the relative frequency.

We're given that the coins were tossed a total of $6,800$ times.
This is our total sample size.
Super important number!

Look at the table!
We're looking for the outcomes where the first coin is heads.
That's HH and HT.

The table tells us HH happened $1,800$ times and HT happened $1,650$ times.
Let's add those up!

$1,800 + 1,650 = 3,450$ So, the first coin was heads a whopping $3,450$ times!

Relative frequency just means: how often something happened divided by the total number of tries.
It's like figuring out your batting average!

We know the first coin was heads $3,450$ times (from the previous addition), and there were a total of $6,800$ tosses.
So, the relative frequency is: $\frac{3,450}{6,800}$

The problem asks us to round to four decimal places.
Looking at the fifth decimal place, which is $5$ or greater, we round up the fourth decimal place.
So, our final answer is $0.5074$ .

The relative frequency of the first coin landing heads up is $0.5074$ .