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Harry Potter is at Ollivanders Wand Shop. As we all know, the wand must choose the wizard, so Harry cannot make the choice himself. He interprets the wand selection as a random process so he can determine the probabilities of different outcomes.



The wood types available are holly, elm, maple, and wenge. The core materials on offer are phoenix feather, unicorn hair, dragon scale, raven feather, and thestral tail.



Let  A  be the event that Harry is chosen by a wand made of holly and let  B  be the event that he is chosen by a wand with a dragon scale core.



What is P(A or B), the probability that Harry is chosen by a wand made of holly or that he is chosen by a wand with a dragon scale core?  


















































           
  Phoenix feather Unicorn hair Dragon scale Raven feather Thestral tail
Holly Holly Phoenix Holly Unicorn Holly Dragon Holly Raven Holly Thestral
Elm Elm Phoenix Elm Unicorn Elm Dragon Elm Raven Elm Thestral
Maple Maple Phoenix Maple Unicorn Maple Dragon Maple Raven Maple Thestral  
Wenge Wenge Phoenix Wenge Unicorn Wenge Dragon Wenge Raven Wenge Thestral

 May 29, 2014

Best Answer 

 #2
avatar+33661 
+8

There are 20 options in total, 5 with holly, 4 with dragon scale.  However, there is one with both holly and dragon scale, so, to avoid double-counting that one, we have 5 + 4 - 1 = 8 possibilities.  So the overall probability is 8/20 = 2/5 = 0.4.

 May 29, 2014

3+0 Answers

 #1
avatar+1006 
+8

As a Potterhead, this Peeves me. The only cores are the heartstrings of a dragon, the feather of a phoenix, and the hair of a unnicorn.

 

Holly wood is 5/20, or 1/4

Dragon scale is 4/20, or 1/5

 

Add the two together.

 

5/20 + 4/20 = 9/20

 

However, do consider that there is one chance of those 'nine' that it can be both, and since the problem asks for 'or', take that out.

 

9/20 - 1/20 = 8/20 = 2/5

 

P(A or B) = 9/20

 May 29, 2014
 #2
avatar+33661 
+8
Best Answer

There are 20 options in total, 5 with holly, 4 with dragon scale.  However, there is one with both holly and dragon scale, so, to avoid double-counting that one, we have 5 + 4 - 1 = 8 possibilities.  So the overall probability is 8/20 = 2/5 = 0.4.

Alan May 29, 2014
 #3
avatar
+5

The equation should be rewritten as

$$P(A or B) = P(A) + P(B) - P(A and B)$$

 May 29, 2014

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