please i need help with my HW

#1
hello

i have question in my home work that i was tried to solve it but unfortunate i can't

the question:

Harrison Water Sports has three retail outlets: Seattle, Portland, and Phoenix. The
Seattle store does 50 percent of the total sales in a year, while the Portland store does 35
percent of the total sales. Further analysis indicates that of the sales in Seattle, 20
percent are in boat accessories. The percentage of boat accessories at the Portland store
is 30 and the percentage is 25 at the Phoenix store. Overall, the probability that a sale by
Harrison Water Sports will be for a boat accessory is

my answer:

s= seattle
p= portland
h= phoenix

total sales= p(s)= 0.5 , p=(p)=0.35 , p(h)=1- p(s)+p(p)=1-0.85=0.15
boat accessories= p(s)= 0.2 , p(p)= 0.3 , p(h)= 0.25

i have sum total sales together = 1

and boat accessories = 0.75

0.75/1=0.75

* i found the answer only in the internet and it was 0.2425

which mean that my answer is wrong

i need help please how did they found 0.2425 ???
 

SiBorg

New Member
#2
If total sales = 1

Harrison does 50%, portland does 35%

Therefore Harrison sales =0.5

Portland sales = 0.35

Pheonix sales = 0.15

Then multiply each store's total sales by percentage sales in boat accessories (i'm assuming that the last 2 figures are percent sales not percent accessories)

0.5 x 0.2 = 0.1

0.35 x 0.3 = 0.105

0.15 x 0.25 = 0.0375

Add together to get 0.2425

Hope this helps
 
Last edited:
#3
The posted solution is correct, but make sure that you get the principle how this was calculated.

This has something to do with conditional probabilities.
Lets say
S = Seattle, P = Portland, H = Phoenix.

Then you have the total sales of each:
P(S) = 0.5
P(P) = 0.35
P(H) = 0.15

And the conditional probabilities: the accessories sales given the total sales
P(A|S) = 0.2
P(A|P) = 0.25
P(A|H) = 0.30

And the sum of those, i.e. P(A) is
P(A) = P(A and S) + P(A and H) + P(A and P)

and each of these eventes is defined by
P(A and S) = P(A|S) * P(S) = 0.2 * 0.5 = 0.1
P(A and P) = P(A|P) * P(P) = 0.3 * 0.35 = 0.15
P(A and H) = P(A|H) * P(H) = 0.15 * 0.25 = 0.0375

And voila, you'll get 0.2425 if you add them all together

P(A) = P(A and S) + P(A and H) + P(A and P) = 0.1 + 0.15 + 0.0375 = 0.2425