How to Calculate Overall Chance

Hi, I'm curious about to calculate overall chance in percentage. For instance, I have 3 Boxes with the following chances to appear:

Box 1 - 30%
Box 2- 60%
Box 3 - 10%

And within Box 3, there is an additional chance that it drops one of 3 following items with a chance:

Item 1 - 30%
Item 2 - 60%
Item 3 - 10%

How do I calculate the total percent chance of Item 3 dropping?

Thanks!

-Kaz

RavenOfBlackRose said:

For instance, I have 3 Boxes with the following chances to appear:
Box 1 - 30%________ Box 2- 60%________ Box 3 - 10%

And within Box 3, there is an additional chance that it drops one of 3 following items with a chance:
Item 1 - 30%________ Item 2 - 60%________ Item 3 - 10%
How do I calculate the total percent chance of Item 3 dropping?

Click to expand...

Hint the portability an item appearing is 0.1. Why is that?

What is the portability the item is \(\displaystyle I_3~?\)

pka said:

Hint the portability an item appearing is 0.1. Why is that?

What is the portability the item is \(\displaystyle I_3~?\)

Click to expand...

Oh, I should probably also mention that a box and an item will always appear / drop, it's just the weightings will be different. I'm just curious to know how I could calculate the percent chance of Item 3 dropping in this scenario.

As an additional hint, you might consider a standard deck of cards. Suppose you draw the top card. What is the probability that card is a Spade? What is the probability that card is a King? Putting those two together, what is the probability that card is the King of Spades? How did you arrive at this answer? What happens if you use the same method in your actual question?