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Help with a simple math problem?

 
 
Reply Wed 10 Oct, 2012 03:01 pm
http://i.imgur.com/50OVq.jpg

why is the answer 1/64?

shouldn't it be like this:

1/4*1/4*1/4*1/4=1/256
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Type: Question • Score: 3 • Views: 4,480 • Replies: 8
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timur
 
  1  
Reply Wed 10 Oct, 2012 03:31 pm
@Anonymous1234567890,
No, because there's four possibilities that they all select the same tire.

Then you have: 4/4^4=1/64
Anonymous1234567890
 
  1  
Reply Wed 10 Oct, 2012 09:57 pm
@timur,
So, what's the numerator? The number of students? What's the denominator? the number of tires? What does the ^4 signify or represent? Sorry, I need to understand this so that I can get it right on my exam.
Ticomaya
 
  1  
Reply Wed 10 Oct, 2012 10:47 pm
@Anonymous1234567890,
4/256 = 1/64

("4^4" means 4 to the 4th power)
Anonymous1234567890
 
  1  
Reply Wed 10 Oct, 2012 10:49 pm
@Ticomaya,
Where'd the 4 come from? What does that represent? The number of students?
Yahto
  Selected Answer
 
  2  
Reply Wed 10 Oct, 2012 11:00 pm
@Anonymous1234567890,
You can go about it an alternative way.

So there are P1, P2, P3, P4. The probability that P2 picks the same tire as P1 is 1/4. Similarly for P3 and P4. Therefore the probability that P2, P3, and P4 all pick the same tire as P1 is (1/4)x(1/4)x(1/4) = 1/64.
Anonymous1234567890
 
  1  
Reply Wed 10 Oct, 2012 11:13 pm
@Yahto,
Oh, wow! I get it! Thank you so very much! It all makes sense now!
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markr
 
  1  
Reply Wed 10 Oct, 2012 11:17 pm
@Anonymous1234567890,
Keep in mind that the probability of a desired outcome is the number of ways the desired outcome can occur divided by the total number of possible outcomes.
4^4 is the number of ways the four students can select a tire. This is the total number of possible outcomes. There are 4 ways that all of the students can select the same tire. This is the number of ways the desired outcome can occur. Therefore, the probability is 4/4^4 = 1/4^3.
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raprap
 
  1  
Reply Thu 11 Oct, 2012 07:08 am
@Anonymous1234567890,
You have four tires A,B,C & D. The first student picks a tire, any tire--the reminin three students pick the same tire.

The possibilities are
AAAA, BBBB, CCCC & DDDD

the first students pick is 4/4, the remaining three are 1/4

AAAA is 1/4^4, BBBB is 1/4^4, CCCC is 1/4^4 & DDDD is 1/4^4

adding them up is the P(E), 4(1/4^4)=1/4^3

Rap
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