Combined skill rolls

[zrestrail]

Hello everyone,  I’m reading through the rules and am a little confused on combined skill rolls.  In the book it reads “Harvey has only 10% skill in both mechanical repair and electrical repair.  The chance of success when making one dice roll and comparing it to both skills simultaneously is 10%.  If two separate rolls were made first against mechanical repair and then against electrical repair, the chance of succeeding in both would be 1%.”

I am confused as to where the 1% comes from.  Can anyone help me out?

[Nick Brooke]

Simple probability. If he needs to succeed in both rolls, he has a (10% of 10%) = 1% chance of doing so.

[Nick Brooke]

Nine times out of ten, he fails the first roll. One time in ten, he succeeds in the first roll… but then there’s a 90% chance he’ll fail the second. Failing either is a wipe-out. See?

[zrestrail]

1 minute ago, Nick Brooke said:

Simple probability. If he needs to succeed in both rolls, he has a (10% of 10%) = 1% chance of doing so.

So if he a 20% and a 30% would that = 10%?

[Nick Brooke]

This isn’t hard. The chance of making both rolls is 0.2 x 0.3 = 0.06, or 6%.

[EricW]

Probability is fun, well worth reading an introductory book.

Some of it is very non-intuitive. For example, if you have a 10% chance of succeeding and you have 10x attempts, your success probability is not 100%. 

In this case you have to multiply the failure probabilities, so:

90% (chance of failure) x 90% x 90% x 90% x 90% x 90% x 90% x 90% x 90% x 90% = 35% chance you won't succeed after 10 attempts. Even after say a million attempts, you have a small chance of failure.

Even less intuitive, say someone presents you with 10 boxes, one of which contains a prize. The game master asks you to pick a box. Then the game master throws away all the boxes except the box you picked, and one other box, and asks you if you want to stick to your original choice, or pick the other box. In this case it always makes sense to pick the other box. Even though you now only have two choices, the history of how you arrived at that choice matters - it is far more likely the prize is in the other box (90%), than the original box you picked (10%). The reason - the probability you picked the right box on your first choice is still only one in 10, 10%, so the probability the other box contains the prize must be 90%.

All good fun. 

Edited August 31, 2022 by EricW

[AlHazred]

Sure, it seems fun. But then you get into the weird edge-cases like the Monty Hall problem, and all common sense goes out the window!