Probabilty with random variable

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  • #1
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Homework Statement


A couple is expecting the arrival of a new boy. They are deciding on a name
from the list S = { Steve, Stanley, Joseph, Elija }. Let X(ω) = first letter in
name. Find Pr(X = S).


Homework Equations





The Attempt at a Solution


Ok the answer is 2/3. How is it 2/3? Shouldnt it be 1/2?
 

Answers and Replies

  • #2
Ray Vickson
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Homework Statement


A couple is expecting the arrival of a new boy. They are deciding on a name
from the list S = { Steve, Stanley, Joseph, Elija }. Let X(ω) = first letter in
name. Find Pr(X = S).


Homework Equations





The Attempt at a Solution


Ok the answer is 2/3. How is it 2/3? Shouldnt it be 1/2?

I would say it is 1/2, assuming that each of the names in S is equally likely.
 
  • #3
haruspex
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Ok the answer is 2/3. How is it 2/3? Shouldnt it be 1/2?
Strange.. are you sure you have quoted the whole question word-for-word?
 
  • #4
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I remember having seen this exact same question in a preparation exam for P/1.

I remember it because the solution said 2/3 and it was obviously wrong. :p
 
  • #5
HallsofIvy
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IF that is the full statement of the problem, it is incomplete. It must say, at the least, that the four names on the list are "equally likely".
 
  • #6
Mentallic
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Could Elija be a girl's name and maybe this has something to do with it? Out of the set of 4 names, if Elija is never going to be chosen since they're expecting a boy, then we actually have 2/3 of the possible names starting with S.
 
  • #7
LCKurtz
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Could Elija be a girl's name and maybe this has something to do with it? Out of the set of 4 names, if Elija is never going to be chosen since they're expecting a boy, then we actually have 2/3 of the possible names starting with S.

I agree. That answer certainly suggests a conditional probability question which likely has been incompletely stated.
 
  • #8
NascentOxygen
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Could Elija be a girl's name and maybe this has something to do with it? Out of the set of 4 names, if Elija is never going to be chosen since they're expecting a boy, then we actually have 2/3 of the possible names starting with S.
Some sites list it as a boy's name, others as a girl's. This site says it's about as likely to be for one as for the other. http://www.gpeters.com/names/baby-names.php?name=Elija

So that doesn't help much, does it?
 
  • #9
Mentallic
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Some sites list it as a boy's name, others as a girl's. This site says it's about as likely to be for one as for the other. http://www.gpeters.com/names/baby-names.php?name=Elija

So that doesn't help much, does it?

Let's assume that this particular couple considers it to be a girl's name :wink:

It's a fair assumption to make seeing as how poorly constructed the question is.
 

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