Question 1170276: An online designer clothing marketplace purchases items from Kenneth Cole, Michael Kors and Vera Wang. The most recent purchases are shown here:
Product Kenneth Cole Micheal Kors Vera Wang
Dresses 26 57 20
Jeans 64 73 20
If one item is selected at random, find theses probabilities, expressed as reduced fractions:
(a) It was purchased from Micheal Kors or Vera Wang.
The Probability that the item selected was purchased from michael kors or vera wang is________
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this probability problem step by step.
**1. Calculate the Total Number of Items**
First, we need to find the total number of items purchased:
Total items = 26 (Kenneth Cole dresses) + 57 (Michael Kors dresses) + 20 (Vera Wang dresses) + 64 (Kenneth Cole jeans) + 73 (Michael Kors jeans) + 20 (Vera Wang jeans)
Total items = 26 + 57 + 20 + 64 + 73 + 20 = 260
**2. Calculate the Number of Items Purchased from Michael Kors or Vera Wang**
Next, we calculate the number of items purchased from Michael Kors or Vera Wang:
Michael Kors items = 57 (dresses) + 73 (jeans) = 130
Vera Wang items = 20 (dresses) + 20 (jeans) = 40
Michael Kors or Vera Wang items = 130 + 40 = 170
**3. Calculate the Probability**
Finally, we calculate the probability by dividing the number of items purchased from Michael Kors or Vera Wang by the total number of items:
Probability = (Number of Michael Kors or Vera Wang items) / (Total items)
Probability = 170 / 260
**4. Reduce the Fraction**
Now, we reduce the fraction to its simplest form. Both 170 and 260 are divisible by 10:
170 / 10 = 17
260 / 10 = 26
So the fraction is 17/26. This fraction cannot be further reduced.
**Answer:**
The probability that the item selected was purchased from Michael Kors or Vera Wang is 17/26.
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