A riddle my brother gave me today (page 2)

snowbird

I'm with Doe.

What precludes a second boy from being born on a Tuesday?

Syl

bohm

Changeling - thats very much true, but just assume the wife generate children who are boys with 1/2 probability independent on what sex the other children she has given birth to has.

John Doe

The more you have of one gender the better the chances of having more of the same... It increases exponentially...I think...

This is not correct.

For background, I was a math major with an A grade in advanced statistics, so I do know a little about the subject.

Take something with a 1/2 probability of occuring, say a coin toss coming up heads. The probability of tossing a coin three times and having heads come up each time is the probability of getting heads 1 time multiplied by three. i.e., 1/2 x 1/2 x 1/2, or 1/8. To illustrate, let's plot all the possible combinations.

h h h

h h t

h t h

h t t

t h h

t h t

t t h

t t t

That's 8 possible combinations, of which only 1 is all heads. So, our math checks.

This is not the same as saying a man rolls a coin three times, and the first two times are heads. What is the probability of the third roll being heads?

The facts in this scenario have already eliminated all possibilities that do not have heads in the first two rolls. So, taking our rolls from before with bold deleting impossible answers:

h h h

h h t

h t h

h t t

t h h

t h t

t t h

t t t

We see that there are only two possible outcomes left in this scenario. So, the chances of the third roll being heads are 1/2. Make sense?

changeling

It's the male who determines the gender...

purplesofa

I had four boys before I had a girl.

Two of the boys are twins.

Three of the boys were born on a Friday.

One was due on a Tuesday but was born on Sunday.

The girl was born on Wednesday.

Just saying.

bohm

Snowbird, Doe: Both children may be born on tuesday. All we know is that at least one of his 2 children is a boy born on a tuesday.

snowbird

Got it!

So, from the info provided, the probability that the other is a boy is 50/50, Tuesday notwithstanding.

Syl

bohm

Side note for changeling: You are right, ff one assume a given couple generate boys with a probability a, the more boys they have (compared to girls) the higher our estimate of a will be, and we will estimate the probability their next children is a boy to be higher. a does not increase exponentially, though.

In the problem, we neglect this effect and assume a=1/2 for both births. Ie. i ask the problem under the most simple assumptions.

changeling

Ask "The Silence" she's smart... :)

bohm

Snowbird: Albert is right - its lower than 1/2.

A riddle my brother gave me today

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