- #1

- 474

- 66

All steps look correctly, but the result does not make any sense.

I'm ok with the part about frogs, but not so with the boy/girl computation.

To sum it up:

1) I have two children and at least one of them is a boy. What is a probability I have a girl?

Answer: 2/3

2) I have two children and at least one of them is a boy

*who was born on Tuesday*. What is the probability I have a girl?

Answer: ~52%

It does not make any sense... to me anyway.

Whatever day of week I say, it tells you nothing about the boy/girl status, does it?

If I said the boy was born on January 1, 2001, would it shift the probability even closer to 50%? How is that possible?

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If you don't want to watch the video:

1) out of the 4 equally probable possibilities ##BB##, ##BG##, ##GB##, ##GG##, the ##GG## is crossed out, leaving 2 of 3 cases containing G.

2) out of the 14^2 equally probable cases ##B_{Monday}B_{Monday}## .. ##G_{Sunday}G_{Sunday}##, we have:

7 cases ##B_{Tuesday}B_{any}##,

6 cases ##B_{not\ Tuesday}B_{Tuesday}##

7 cases ##B_{Tuesday}G_{any}##,

7 cases ##G_{any}B_{Tuesday}##.

So, to have a G, we have (7+7)/(7+6+7+7)=14/27 ~ 52%.