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You manage an ice cream stand with two flavors cherry and…

You manage an ice cream...
You manage an ice cream stand with two flavors: cherry and banana. You only receive ice cream early each morning, so there is a risk you will run out of ice cream during the day. Based on experience, you know that on any given day there is a 10% chance you will run out of cherry and a 12% chance you will run out of banana. There is a 86% chance that neither flavor will run out on a given day. If you run out of cherry on a given day, what is the probability that you will run out of banana on the same day, given you have run out of cherry?
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Answered in 11 minutes by:
6/29/2010
Stevewh
Stevewh, Bachelor's Degree
Category: Math Homework
Satisfied Customers: 7,610
Experience: Statistics degree
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Let A="run out of cherry"
Let B= "run out of banana"

P(A)=0.1
P(B)=0.12

P(not A and not B)=0.86

P(B/A)=P(A,B)/P(A)


P(not A,B)+P(not A,not B)=P(not A)

P(not A,B)+0.86=0.9

P(not A,B)=0.04

P(A,not B)+P(not A,not B)=P(not B)

P(A,not B)+0.86=0.88

P(A,not B)=0.02

Finally:


P(A,B)+P(not A,B)+P(A,not B)+P(not A,not B)=1

P(A,B)+0.04+0.02+0.86=1

P(A,B)=0.08

P(B/A)=0.08/0.1=0.8

Answer: P(B/A)=0.8

Bonus is greatly appreciated

Thanks

Steve
Stevewh
Stevewh, Bachelor's Degree
Category: Math Homework
Satisfied Customers: 7,610
Experience: Statistics degree
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I can´t make a deal (it´s a site rule)

But feel free to request me writing "For Steve" if you need more questions

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Steve
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