Jack Daniels
Fort Dix, New Jersey, United States
The question is "if you flip a coin twice, and at least one coin lands heads, what is the probability both coins land heads?" This is a conditional probability question, meaning in calculating the probability both coins land heads, we consider only the cases where at least one coin landed heads. If you flip two coins, there are four equally likely outcomes: heads+heads, heads+tails, tails+heads, and tails+tails. We ignore the tails+tails outcome because of the condition. Out of the remaining three outcomes, there is only one in which both coins landed heads. Therefore the answer is 1/3.

Be warned that there are very similar-sounding questions to which the answer is 1/2. For example, consider the scenario in which two coins are flipped, and I randomly choose one of them to look at. Given that it is heads, what is the probability the other coin is heads? This seems like the same question as our original question, but it is not. Here we have to consider eight equally likely outcomes: heads+heads+picked_left, heads+heads+picked_right, heads+tails+picked_left, heads+tails+picked_right, tails+heads+picked_left, tails+heads+picked_right, tails+tails+picked_left, and tails+tails+picked_right. Our condition that the seen coin be heads narrows the possibilities down to four outcomes: heads+heads+picked_left, heads+heads+picked_right, heads+tails+picked_left, and tails+heads+picked_right. Of these four outcomes, there are two in which both coins are heads.
The question is "if you flip a coin twice, and at least one coin lands heads, what is the probability both coins land heads?" This is a conditional probability question, meaning in calculating the probability both coins land heads, we consider only the cases where at least one coin landed heads. If you flip two coins, there are four equally likely outcomes: heads+heads, heads+tails, tails+heads, and tails+tails. We ignore the tails+tails outcome because of the condition. Out of the remaining three outcomes, there is only one in which both coins landed heads. Therefore the answer is 1/3.

Be warned that there are very similar-sounding questions to which the answer is 1/2. For example, consider the scenario in which two coins are flipped, and I randomly choose one of them to look at. Given that it is heads, what is the probability the other coin is heads? This seems like the same question as our original question, but it is not. Here we have to consider eight equally likely outcomes: heads+heads+picked_left, heads+heads+picked_right, heads+tails+picked_left, heads+tails+picked_right, tails+heads+picked_left, tails+heads+picked_right, tails+tails+picked_left, and tails+tails+picked_right. Our condition that the seen coin be heads narrows the possibilities down to four outcomes: heads+heads+picked_left, heads+heads+picked_right, heads+tails+picked_left, and tails+heads+picked_right. Of these four outcomes, there are two in which both coins are heads.
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2 Feb, 2025 @ 4:19pm 
I am an ant, I follow the line of pheromones till death and if it disappears I will wander forevermore... Signed by ban
17 Nov, 2024 @ 3:58am 
i don't look down on others because i'm white, i really don't care about that. nor do i hate women because i'm a dude and dudes are supposed to be better or something. the primary thing that sets me apart from most of my peers, is my parents' talent for making money. my parents (especially my mom) were so good at making money, that i have consistently been able to afford nice things, which makes me happy.
7 Oct, 2024 @ 5:07am 
yes?
2 Oct, 2024 @ 8:12am 
nietogo
2 Oct, 2024 @ 8:12am 
nietogo
30 Sep, 2024 @ 8:48am 
mahjong soulful