>>12398250Ok imma make this real easy for your mentally deprived ass.
Baby steps.
The outcome for each coin is independant.
We assume the coins are balanced and therefore we have 50% for each side of a coin.
Let's deal with one coin first and then the second.
First coin.
50% chance it's tails, 50% chance it's heads.
Those probabilities also cover the total set of all following events, i.e. 50% of the following outcomes each.
The second coin also has 50% chance of landing on either side
Given the first coin is tails, the second coin is either 50% tails, 50% heads.
Same thing if the first coin is heads.
Regarding the overall probability without any given condition, the probabilities for each coin are multiplied.
First coin is tails and second coin is tails
(50% * 50%) = 25%
First coin is tails and second coin is heads
(50% * 50%) = 25%
First coin is heads and second coin is tails
(50% * 50%) = 25%
First coin is heads and second coin is heads
(50% * 50%) = 25%
Probability of two tails = 25%
Probability of two heads = 25%
Probability of one heads one tails = 25% + 25% = 50%
Probability of at least one heads? = 25% + 25% + 25% = 75%
Probability of two heads given at least one heads? = 25% / 75% = 1/3
