>>12078149Yes, which means it's "given that the first ball selected is gold". This isn't hard, anon.
There are six possible outcomes, before any conditions.
You pick box 1 and choose gold 11, forcing you to take gold 12
You pick box 1 and choose gold 12, forcing you to take gold 11
You pick box 2 and choose gold 21, forcing you to take silver 22
You pick box 2 and choose silver 22, forcing you to take gold 21
You pick box 3 and choose silver 31, forcing you to take silver 32
You pick box 3 and choose silver 32, forcing you to take silver 31
Let's consider both cases
>"given that the first ball selected is gold" (correct interpretation)There are only three possible outcomes where the first ball chosen is gold.
You pick box 1 and choose gold 11, forcing you to take gold 12
You pick box 1 and choose gold 12, forcing you to take gold 11
You pick box 2 and choose gold 21, forcing you to take silver 22
Of these three, the first two result in the second ball being gold
The probability of the second ball being gold is 2/3
>"given that you select from a box with at least one gold" (incorrect interpretation)As only box 1 and 2 contain at least one gold, there are four possible outcomes.
You pick box 1 and choose gold 11, forcing you to take gold 12
You pick box 1 and choose gold 12, forcing you to take gold 11
You pick box 2 and choose gold 21, forcing you to take silver 22
You pick box 2 and choose silver 22, forcing you to take gold 21
Of these four, only three result in the second ball being gold, resulting in a probability of 3/4.
>conclusionNotice how in both of these interpretations (former being correct, latter being incorrect but understandable), neither answer is 1/2.
Therefor, you're smoothbrained mongoloid either way for thinking that 1/2 is the correct answer.
Q.E.D.
