Let's say, hypothetically speaking, you met someone who told you they had two children, and one of them is a girl. What are the odds that person has a boy and a girl?
Your 1 million coins example is wrong. The question would be 1 million coins were tossed. 999,999 were tails. What’s the chance the other one was heads?
I’m not going to solve this problem but the key is that the single heads result doesn’t have to be the 1,000,000th toss - it could be the 999,998th toss or 57th toss or any single toss as long as the other 999,999 are tails. So the probability will not be 50%.
@Sam A.
The 999,999 coins that you placed on the table have NO bearing on the one you are actually flipping. The 999,999 are the given, known information. The probability of the coin you flipped (unknown information) is still 50%.
2 coins were tossed. One is heads. What’s the probability that the other is tails?
Assume coin on left is heads. Then the other coin has 50% chance of heads and 50% tails.
BUT the question didn’t say the coin on the left was heads. So let’s now assume that the coin on the right is heads, then the coin on the left is 50% chance of heads and 50% tails.
Step 3 is wrong. The problem is that the heads-heads combination was double-counted. The times in 1) when we got heads-heads and the times in 2) when we got heads-heads were the SAME events, so we should only count them once. So to adjust: (250%) / (450% - 50%) = 100 / 150 = 2/3
For those who are confused if you remove the order than GB and BG are the same thing (because there are is just a B and a G somewhere in the pot, they are not ordered in any way).
For those who are confused if you remove the order than GB and BG are the same thing (because there are is just a B and a G somewhere in the pot, they are not ordered in any way).
So you cannot call BG and GB separate solutions.
If you call them separate solutions then you are saying the order matters. The question did not say the order mattered, so these are not separate solutions.
I am convinced that the common voodoo beliefs portrayed as statistics and logic are diametrically opposed (IE, Statistics theory is fundamentally flawed).
For those who are confused if you remove the order than GB and BG are the same thing (because there are is just a B and a G somewhere in the pot, they are not ordered in any way).
So you cannot call BG and GB separate solutions. They would be the SAME SOLUTION.
If you call them separate solutions then you are saying the order matters. The question did not say the order mattered, so these are not separate solutions.
Ok, I was wrong. I didn’t believe that the child’s age makes a difference but it does. There are two working possibilities out of three. Guess I should have though that through more carefully.