# Probabilty with random variable

## 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).

## The Attempt at a Solution

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

Ray Vickson
Homework Helper
Dearly Missed

## 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).

## 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.

haruspex
Homework Helper
Gold Member
2020 Award
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?

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

HallsofIvy
Homework Helper
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".

Mentallic
Homework Helper
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.

LCKurtz
Homework Helper
Gold Member
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.

NascentOxygen
Staff Emeritus
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?

Mentallic
Homework Helper
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

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