Hello one and all. I could use a little guidance here on a probability problem.(adsbygoogle = window.adsbygoogle || []).push({});

Box #1 containsablack balls andbwhite balls while box #2 containscblack balls anddwhite balls. A ball is chosen randomly from box #1 and placed in box #2. A ball is then randomly chosen from box #2 and placed in box #1. What is the probability that box #1 still hasablack balls andbwhite balls?

Okay, from that I come up with the following:

Let Random Variable X1 = a black ball is transferred to box #2 from box #1

Let R.V. X2 = a white ball is transferred to box #2 from box #1

Let R.V. Y1 = a black ball is transferred to box #1 from box #2

Let R.V. Y2 = a white ball is transferred to box #1 from box #2

[tex]P(X_1) = \frac{a}{a+b}[/tex] and [tex]P(X_2) = \frac{b}{a+b}[/tex]

[tex]P(Y_1 \mid X_1) = \frac{c+1}{c+d+1}[/tex] and [tex]P(Y_1 \mid X_2) = \frac{c}{c+d+1}[/tex]

[tex]P(Y_2 \mid X_1) = \frac{d}{c+d+1}[/tex] and [tex]P(Y_2 \mid X_2) = \frac{d+1}{c+d+1}[/tex]

This is where I get stuck.

I know (for example) that I can define another R.V. to represent, say, a black ball was selected from box #2 (I'll call it R.V. A), and...

[tex]P(A) = P(X_1) \cdot P(Y_1 \mid X_1) + P(X_2) \cdot P(Y_1 \mid X_2)[/tex]

Assuming I'm somewhat on the right track and haven't screwed things up, how would I go about determining the probability that box #1 still hasablack balls andbwhite balls?

Thanks in advance for your enlightenment (and do I need it).

dogma

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Balls in Boxes, Probability Question

Loading...

Similar Threads for Balls Boxes Probability | Date |
---|---|

I Dividing 4 balls over 4 boxes | Jan 26, 2018 |

I Statistical problem of drawing colored balls from boxes | Apr 12, 2017 |

Dragging colored balls off box in succession | Apr 15, 2015 |

Distribution of balls in a box (with a twist) | May 15, 2014 |

Balls in a box shaking experiment | Oct 2, 2012 |

**Physics Forums - The Fusion of Science and Community**