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Online marketplaces have become a popular way for individuals to buy and sell miscellaneous items. The table to the right shows the number of days products stayed active​ (not sold) on one of these sites and also the price range of the items. Complete parts a through c below.Price Range1-7 Days8-30 DaysOver 30 DaysTotal Under $2001181327158$200-$50019615395444$501-$1,0004055301791114Over $1,00012113836295Total 8408343372011b. Is the event​ "1-7 days on the​ website" independent of the price range​ $200-$500?How do I fill in the blanks from the choices provided?(Yes or No) because the (Sum or Product) of the probabilities of the two events (Does or Does Not) equal the (Joint or Conditional) probability.

Question

Online marketplaces have become a popular way for individuals to buy and sell miscellaneous items. The table to the right shows the number of days products stayed active​ (not sold) on one of these sites and also the price range of the items. Complete parts a through c below.

Price Range 1-7 Days 8-30 Days Over 30 Days Total 
Under $200 118 13 27 158
$200-$500 196 153 95 444
$501-$1,000 405 530 179 1114
Over $1,000 121 138 36 295
Total  840 834 337 2011

b. Is the event​ "1-7 days on the​ website" independent of the price range​ $200-$500?

How do I fill in the blanks from the choices provided?

(Yes or No) because the (Sum or Product) of the probabilities of the two events (Does or Does Not) equal the (Joint or Conditional) probability. 

 

check_circleAnswer
Step 1

Let A be the event that product stayed active on website for 1-7 days

Let B be the event that product is in the price range $200-$500

Probability of event A = P(A) = 840/2011

Probability of event B= P(B) = 444/2011

Probability of event A and B = P(AnB) = 196/2011

A
C
D
1 Price Range
2 Under $200
3 $200-$500
|$501-$1,000
5 Over $1,000
Total
1-7 Days
8-30 Days Over 30 Days
118
158
13
27
196
444
153
95
405
530
179
1114
4
295
121
138
36
840
2011
6 Total
834
337
7
C
help_outline

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A C D 1 Price Range 2 Under $200 3 $200-$500 |$501-$1,000 5 Over $1,000 Total 1-7 Days 8-30 Days Over 30 Days 118 158 13 27 196 444 153 95 405 530 179 1114 4 295 121 138 36 840 2011 6 Total 834 337 7 C

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Step 2

If 2 events are independent then , P(AnB) = P(A) * P(B)

P(A)*P(B) = 840/2011  * 444/2011  = 0.09222

P(AnB) = 196...

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