1. You are on Etsy, an online marketplace to sell homemade goods, when you come
ID: 3297830 • Letter: 1
Question
1. You are on Etsy, an online marketplace to sell homemade goods, when you come across a vendor that sells sweaters. One of the services they offer is, if you pay $15, they will send you a mystery sweater in your size. To calm the nerves of potential customers, the vendor provides the proportion of their stock that is each color: 15% blue, 20% green, 35% red, 10% purple, and 20% yellow. Even though you don’t know what sweater you will be sent, you are hoping it will be red.
a) What is the random variable in this scenario?
b) What distribution would this follow? Make sure to specify the values of the parameter(s).
c) What is the probability that the sweater you are sent is red?
2. Same scenario as in Question 1. However, you decide to order 6 sweaters from this vendor. Your plan is to keep all the red sweaters and give the others to your friends.
a) What is the random variable in this scenario?
b) What distribution would this follow. Make sure to specify the values of the parameter(s).
c) What is the probability that you will get exactly 4 red sweaters?
d) What is the probability you will at most 2 red sweaters?
e) How many red sweaters might you expect to receive?
3. Same scenario as Question 1. However you decide to keep ordering mystery sweaters from this vendor until you get a red one.
a) What is the random variable in this scenario?
b) What distribution does this follow? Make sure to specify the values of the parameter(s).
c) What is the probability that you will get a red sweater on the 7th order?
d) What is the probability you will need to place at least 3 orders but at most 6 orders to get the first red sweater?
e) How many orders would you expect to place in order to get the first red sweater?
Explanation / Answer
1. You are on Etsy, an online marketplace to sell homemade goods, when you come across a vendor that sells sweaters. One of the services they offer is, if you pay $15, they will send you a mystery sweater in your size. To calm the nerves of potential customers, the vendor provides the proportion of their stock that is each color: 15% blue, 20% green, 35% red, 10% purple, and 20% yellow. Even though you don’t know what sweater you will be sent, you are hoping it will be red.
a) What is the random variable in this scenario?
b) What distribution would this follow? Make sure to specify the values of the parameter(s).
c) What is the probability that the sweater you are sent is red?
Answer:
a) Here the random variable we are studying is the colour of the mystery sweater that will be received by the customer.
b) This follows a discrete random distribution which is given as:
Let the random variable be rerepsented by the notation X. Then we have the distribution here as:
c) Probability that the sweater sent is red would be given as:
P( X = red ) = 0.35
X Blue Green Red Purple Yellow P(X=x) 0.15 0.20 0.35 0.1 0.2Related Questions
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