EricW
Senior HTF Member
- Joined
- Jan 1, 2001
- Messages
- 2,308
hey guys, i need some input as i've been going back and forth with my brother-in-law with this all night. it a probabilities question involving three coins.
here is the scenario.
1) you have three coins in hand
2) you throw all three in the air
3) the three coins fall to the ground.
4) before knowing the orientation of any coins, you cover one at random.
5) *IF* the 2 exposed coins are both heads, what is the probability that the hidden coin will be a Head?
my answer was that it is 50/50 whether the hidden coin is H or T.
here's the proof: below is the outcome table.
-along the left are the possible outcomes of a coin toss.
-along the top are the possible positions of the "hiding hand"
-there are only 6 possible outcomes which we would consider (red boxes - where both exposed coins are H's)
-of those 6 outcomes, 3 have a hidden Head and 3 have a hidden Tail.
is this sound logic? if i'm missing something please tell me.
oh by the way, the loser has to buy Boardwalk Empire on Blu-ray
here is the scenario.
1) you have three coins in hand
2) you throw all three in the air
3) the three coins fall to the ground.
4) before knowing the orientation of any coins, you cover one at random.
5) *IF* the 2 exposed coins are both heads, what is the probability that the hidden coin will be a Head?
my answer was that it is 50/50 whether the hidden coin is H or T.
here's the proof: below is the outcome table.
-along the left are the possible outcomes of a coin toss.
-along the top are the possible positions of the "hiding hand"
-there are only 6 possible outcomes which we would consider (red boxes - where both exposed coins are H's)
-of those 6 outcomes, 3 have a hidden Head and 3 have a hidden Tail.
is this sound logic? if i'm missing something please tell me.
oh by the way, the loser has to buy Boardwalk Empire on Blu-ray