Math / Data & Statistics

Questiononline designer clothing marketplace purchases items from Kenneth Cole, Michael Kors and Vera Wang. The most recent purchases e shown here: \begin{tabular}{|c|c|c|c|} \hline Product & \begin{tabular}{c} Kenneth \\ Cole \end{tabular} & \begin{tabular}{c} Michael \\ Kors \end{tabular} & \begin{tabular}{c} Vera \\ Wang \end{tabular} \\ \hline Dresses & 51 & 37 & 10 \\ \hline Jeans & 75 & 71 & 11 \\ \hline \end{tabular} f one item is selected at random, find these probabilities, expressed as reduced fractions:
Part 1 of 3 (a) It was purchased from Kenneth Cole or it is a dress.
The probability that the item selected was purchased from Kenneth Cole or is a dress is $\frac{173}{255}$ .
Part: $1 / 3$
Part 2 of 3 (b) It was purchased from Michael Kors or Vera Wang.
The probability that the item selected was purchased from Michael Kors or Vera Wang is

Studdy Solution

STEP 1

What is this asking? What's the chance we grab a Kenneth Cole item or a dress, and what's the chance we grab something from Michael Kors or Vera Wang? Watch out! Don't double-count the items that fit both descriptions!

STEP 2

1. Total Items
2. Kenneth Cole or Dress
3. Michael Kors or Vera Wang

STEP 3

Let's add up all the items to find the total!
We have dresses and jeans from three designers.
We're going to add all the numbers together!

STEP 4

$51 + 37 + 10 + 75 + 71 + 11 = 255$ So there are a whopping 255 items in total!

STEP 5

How many items are from Kenneth Cole?
Let's see, $51$ dresses and $75$ jeans.
That's $51 + 75 = 126$ items.

STEP 6

How many dresses are there? $51 + 37 + 10 = 98$ dresses.

STEP 7

Now, some items are both Kenneth Cole and dresses.
We already counted those in both groups, so we need to subtract them once so we don't double-count.
There are $51$ Kenneth Cole dresses.

STEP 8

So, the number of items that are either Kenneth Cole or a dress (or both!) is $126 + 98 - 51 = 173$ .

STEP 9

The probability of picking one of these items is the number of these items divided by the total number of items: $\frac{173}{255}$ .
Woohoo!

STEP 10

How many items are from Michael Kors? $37 + 71 = 108$ items.

STEP 11

How many items are from Vera Wang? $10 + 11 = 21$ items.

STEP 12

Since there's no overlap between these designers (no item is from both Michael Kors and Vera Wang), we can just add them up: $108 + 21 = 129$ items.

STEP 13

The probability of grabbing a Michael Kors or Vera Wang item is the number of these items divided by the total number of items: $\frac{129}{255}$ .
We can simplify this fraction by dividing both the numerator and denominator by 3, which gives us $\frac{43}{85}$ .
Awesome!

STEP 14

(a) The probability of selecting an item from Kenneth Cole or a dress is $\frac{173}{255}$ . (b) The probability of selecting an item from Michael Kors or Vera Wang is $\frac{43}{85}$ .

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Studdy Solution

STEP 1

What is this asking? What's the chance we grab a Kenneth Cole item or a dress, and what's the chance we grab something from Michael Kors or Vera Wang? Watch out! Don't double-count the items that fit both descriptions!

STEP 2

1. Total Items
2. Kenneth Cole or Dress
3. Michael Kors or Vera Wang

STEP 3

Let's add up all the items to find the total!
We have dresses and jeans from three designers.
We're going to add all the numbers together!

STEP 4

$51 + 37 + 10 + 75 + 71 + 11 = 255$ So there are a whopping 255 items in total!

STEP 5

How many items are from Kenneth Cole?
Let's see, $51$ dresses and $75$ jeans.
That's $51 + 75 = 126$ items.

STEP 6

How many dresses are there? $51 + 37 + 10 = 98$ dresses.

STEP 7

Now, some items are both Kenneth Cole and dresses.
We already counted those in both groups, so we need to subtract them once so we don't double-count.
There are $51$ Kenneth Cole dresses.

STEP 8

So, the number of items that are either Kenneth Cole or a dress (or both!) is $126 + 98 - 51 = 173$ .

STEP 9

The probability of picking one of these items is the number of these items divided by the total number of items: $\frac{173}{255}$ .
Woohoo!

STEP 10

How many items are from Michael Kors? $37 + 71 = 108$ items.

STEP 11

How many items are from Vera Wang? $10 + 11 = 21$ items.

STEP 12

Since there's no overlap between these designers (no item is from both Michael Kors and Vera Wang), we can just add them up: $108 + 21 = 129$ items.

STEP 13

The probability of grabbing a Michael Kors or Vera Wang item is the number of these items divided by the total number of items: $\frac{129}{255}$ .
We can simplify this fraction by dividing both the numerator and denominator by 3, which gives us $\frac{43}{85}$ .
Awesome!

STEP 14

(a) The probability of selecting an item from Kenneth Cole or a dress is $\frac{173}{255}$ . (b) The probability of selecting an item from Michael Kors or Vera Wang is $\frac{43}{85}$ .

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Studdy Solution

STEP 1

What is this asking? What's the chance we grab a Kenneth Cole item *or* a dress, and what's the chance we grab something from Michael Kors *or* Vera Wang? Watch out! Don't double-count the items that fit *both* descriptions!

STEP 2

1. Total Items2. Kenneth Cole or Dress3. Michael Kors or Vera Wang

STEP 3

Let's **add up** all the items to find the **total**!We have dresses and jeans from three designers.We're going to add all the numbers together!

STEP 4

51+37+10+75+71+11=25551 + 37 + 10 + 75 + 71 + 11 = 25551+37+10+75+71+11=255 So there are a **whopping 255 items** in total!

STEP 5

How many items are from Kenneth Cole?Let's see, 515151 dresses and 757575 jeans.That's 51+75=12651 + 75 = 12651+75=126 items.

STEP 6

How many dresses are there? 51+37+10=9851 + 37 + 10 = 9851+37+10=98 dresses.

STEP 7

Now, some items are *both* Kenneth Cole *and* dresses.We already counted those in both groups, so we need to subtract them once so we don't double-count.There are 515151 Kenneth Cole dresses.

STEP 8

So, the number of items that are *either* Kenneth Cole *or* a dress (or both!) is 126+98−51=173126 + 98 - 51 = 173126+98−51=173.

STEP 9

The probability of picking one of these items is the number of these items divided by the total number of items: 173255\frac{173}{255}255173​.Woohoo!

STEP 10

How many items are from Michael Kors? 37+71=10837 + 71 = 10837+71=108 items.

STEP 11

How many items are from Vera Wang? 10+11=2110 + 11 = 2110+11=21 items.

STEP 12

Since there's no overlap between these designers (no item is from *both* Michael Kors *and* Vera Wang), we can just add them up: 108+21=129108 + 21 = 129108+21=129 items.

STEP 13

The probability of grabbing a Michael Kors or Vera Wang item is the number of these items divided by the total number of items: 129255\frac{129}{255}255129​.We can simplify this fraction by dividing both the numerator and denominator by 3, which gives us 4385\frac{43}{85}8543​.Awesome!

STEP 14

(a) The probability of selecting an item from Kenneth Cole or a dress is 173255\frac{173}{255}255173​. (b) The probability of selecting an item from Michael Kors or Vera Wang is 4385\frac{43}{85}8543​.

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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.

What is this asking? What's the chance we grab a Kenneth Cole item or a dress, and what's the chance we grab something from Michael Kors or Vera Wang? Watch out! Don't double-count the items that fit both descriptions!

1. Total Items
2. Kenneth Cole or Dress
3. Michael Kors or Vera Wang

Let's add up all the items to find the total!
We have dresses and jeans from three designers.
We're going to add all the numbers together!

$51 + 37 + 10 + 75 + 71 + 11 = 255$ So there are a whopping 255 items in total!

How many items are from Kenneth Cole?
Let's see, $51$ dresses and $75$ jeans.
That's $51 + 75 = 126$ items.

How many dresses are there? $51 + 37 + 10 = 98$ dresses.

Now, some items are both Kenneth Cole and dresses.
We already counted those in both groups, so we need to subtract them once so we don't double-count.
There are $51$ Kenneth Cole dresses.

So, the number of items that are either Kenneth Cole or a dress (or both!) is $126 + 98 - 51 = 173$ .

The probability of picking one of these items is the number of these items divided by the total number of items: $\frac{173}{255}$ .
Woohoo!

How many items are from Michael Kors? $37 + 71 = 108$ items.

How many items are from Vera Wang? $10 + 11 = 21$ items.

Since there's no overlap between these designers (no item is from both Michael Kors and Vera Wang), we can just add them up: $108 + 21 = 129$ items.

The probability of grabbing a Michael Kors or Vera Wang item is the number of these items divided by the total number of items: $\frac{129}{255}$ .
We can simplify this fraction by dividing both the numerator and denominator by 3, which gives us $\frac{43}{85}$ .
Awesome!

(a) The probability of selecting an item from Kenneth Cole or a dress is $\frac{173}{255}$ . (b) The probability of selecting an item from Michael Kors or Vera Wang is $\frac{43}{85}$ .