# Probabilty with random variable

1. Dec 19, 2013

### DotKite

1. The problem statement, all variables and given/known data
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).

2. Relevant equations

3. The attempt at a solution
Ok the answer is 2/3. How is it 2/3? Shouldnt it be 1/2?

2. Dec 19, 2013

### Ray Vickson

I would say it is 1/2, assuming that each of the names in S is equally likely.

3. Dec 19, 2013

### haruspex

Strange.. are you sure you have quoted the whole question word-for-word?

4. Dec 20, 2013

### h6ss

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. Dec 20, 2013

### HallsofIvy

Staff Emeritus
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. Dec 20, 2013

### Mentallic

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. Dec 20, 2013

### LCKurtz

I agree. That answer certainly suggests a conditional probability question which likely has been incompletely stated.

8. Dec 29, 2013

### Staff: Mentor

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. Dec 29, 2013

### Mentallic

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.