Probability Question (1 Viewer)

[seanieg89]

Try this one:
A couple has two children, one of whom is a boy who was born on a Thursday. What is the probability that the other child is also a boy?

(This isn't a lateral thinking question).

Edit:

Although admittedly with more precise wording, the problem messes with the mind less. It is similar to the Monty Hall problem for those who have seen the movie "21".

 

[MrBrightside]

Try this one:
A couple has two children, one of whom is a boy who was born on a Thursday. What is the probability that the other child is also a boy?

(This isn't a lateral thinking question).

What kind of question is that? wtf

 

[Amogh]

You just want us to say 1/2 so that you laugh at us!

I'm not going to spoil it because I googled it
Thanks for the question mate! Twas interesting.

 

[seanieg89]

You just want us to say 1/2 so that you laugh at us!

I'm not going to spoil it because I googled it
Thanks for the question mate! Twas interesting.

Its not as silly as it sounds MrBrightside.

 

[someth1ng]

Try this one:
A couple has two children, one of whom is a boy who was born on a Thursday. What is the probability that the other child is also a boy?

We know that atleast one is a boy.
Possibilities:
Boy, Boy
Boy, Girl
Girl, Boy

Out of these three, they all have equal probability and hence, the probability of another boy is 1/3...maybe...that Thursday is shitting me...now I'm off to Google.

It's actually quite ambiguous...there was still an initial probability that there could be 2 girls (1/4) and that was revealed untrue when you told us there was one boy...okay fuck this.

 

[aundii]

Half. Child genders are independent events, like tossing a coin.

EDIT: If you wanted to do it mathematically...

P(boy boy) = P(1st is a boy) x P(2nd is a boy)
= 1/1 x 1/2
= 1/2

 

[someth1ng]

Half. Child genders are independent events, like tossing a coin.

EDIT: If you wanted to do it mathematically...

P(boy boy) = P(1st is a boy) x P(2nd is a boy)
= 1/1 x 1/2
= 1/2

I have written possible cases above.
BG
GB
BB

There's 1 cases with two boys out of three.

 

[aundii]

I have written possible cases above.
BG
GB
BB

There's 1 cases with two boys out of three.

GB and BG are the same thing because we know that the 1st child is B.

 

[aundii]

GB and BG are the same thing because we know that the 1st child is B.

Read the question wrong, assumed that the first child was male, my bad.

 

[aundii]

Anyway, my answer remains as 1/2; mathematically speaking, gender is always an independent event and the chance of a particular gender is 1/2. Wouldn't make a difference if they couple had 2 kids or 20 kids; the chance that any one of them were male would be 1/2.

 

[someth1ng]

Anyway, my answer remains as 1/2; mathematically speaking, gender is always an independent event and the chance of a particular gender is 1/2. Wouldn't make a difference if they couple had 2 kids or 20 kids; the chance that any one of them were male would be 1/2.

But you were told they have one boy. The answer could be 1/3 or 1/2 but if you actually tested this the result would be closer to 1/3.

 

[aundii]

But you were told they have one boy. The answer could be 1/3 or 1/2 but if you actually tested this the result would be closer to 1/3.

That works with the Monty Hall problem, but we're talking about independent events here; it doesn't matter what we already know, the chances that the other child is a boy is 1/2. The chances that any given child is a boy is ALWAYS 1/2.

 

[someth1ng]

That works with the Monty Hall problem, but we're talking about independent events here; it doesn't matter what we already know, the chances that the other child is a boy is 1/2. The chances that any given child is a boy is ALWAYS 1/2.

Well, if you were to get all the couples with 2 children but remove all of those with 2 girls, you will theoretically be left with equal numbers of:
BG
GB
BB
So if you know you have 1 boy, the odds of the other boy is 1/3. This is only 1/3 because of the information that is given to you but if they were to ask something like "what would the odds of a second child being a boy?" would be obviously 1/2.

 

[seanieg89]

Ignoring the "Thursday" part for now (which in my opinion brings up the most counter-intuitive aspect of the question).

The critical reason why this simpler question has answer 1/3 and not 1/2 is that we are not stipulating order at any stage.
So asking "What is the probability of the other child also being a boy" is very different from asking "What is the probability of the second child being a boy".

The BG/GB/BB approach here works fine.

 

[someth1ng]

Do I like, get kudos for that?

 

[seanieg89]

you have my kudos try the question including the Thursday part though, bonus point if you are able to explain why that makes a difference

 

[someth1ng]

you have my kudos try the question including the Thursday part though, bonus point if you are able to explain why that makes a difference

Yeah...well, I googled it and the answer it gives me hardly makes sense so I doubt I can actually make up my own.

 

[largarithmic]

13/27? you just count the possibilities?

 

[seanieg89]

Yep, so actually not that hard a question apart from being fairly unintuitive. You can replace the property of "birth on Thursday" by an arbitrary property. If the property is rare, your probability will be close to 1/2, if the property is common, your probability will be close to 1/3 .