- #1
Kolmin
- 66
- 0
Homework Statement
There are two boxes:
- in the first one there is 1 red ball,
- in the second one there are 2 balls, 1 red & 1 white.
1st draw: We take a ball from the second box without taking a look at the color and we put it in the first box.
2nd draw: We take a ball from the first box.
The ball is red.
What is the probability of having another red ball in the first box?
Homework Equations
[itex]P(R)[/itex] is the probability of taking a red ball on first draw
[itex]P(r)[/itex] is the probability of having a red ball in the first box after the second draw
[itex]P(R|r)[/itex] is the probability of having taken a Red ball on the first draw, given that we have found a red ball in the first box after the second draw.
[itex]P(r|R)[/itex] is the probability of having a red ball in the first box, given that we took a Red ball on the first draw.
The Attempt at a Solution
I can hardly find something more than Probability to which apply the sentence "it's not my cup of tea":
Actually I am not even sure about the way in which I framed the problem in [2.].
However, if that framework stands, then I would say that:
[itex]P(R)=\frac{1}{2}[/itex]
[itex]P(R|r)=1[/itex]
[itex]P(r|R)=1[/itex]
And here there is the mistake (I am almost sure about it, even if I dont' see why):
[tex]P(r)= \frac{P(R)P(r|R)}{P(R|r)}=\frac{1}{2}[/tex]
Right or wrong?