>>12942367assuming we're getting this information from something like a friend who looks at both coins and tells you at least one is heads, then the answer is 1/3
B represents "both coins landed heads"
O represents "friend tells you at least one coin landed heads"
P(B) = 1/4 # one outcome out of four possibilities {HH}/{HH,HT,TH,TT}
P(O) = 3/4 # three outcomes out of four possibilities {HH,HT,TH}/{HH,HT,TH,TT}
P(O|B) = 1 # always at least one head if both are heads
P(B|O) = P(O|B)*P(B) / P(O) = (1)*(1/4) / (3/4) = 1/3 # bayes rule
if we stretch the wording and it's something like you flip the coins then look at one of them and see a head, the answer is 1/2
O represents "you look at one coin and see a head"
P(B) = 1/4 # as above
P(O) = P(O|HH)*P(HH) + P(O|HT)*P(HT) + P(O|TH)*P(TH) + P(O|TT)*P(TT) = (1)*(1/4) + (1/2)*(1/4) + (1/2)*(1/4) + (0)*(1/4) = 1/2 # law of total probability
PO|B) = 1 # always see a head after checking one coin if both are heads
P(B|O) = P(O|B)*P(B) / P(O) = (1)*(1/4) / (1/2) = 1/2 # bayes rule
easy to confirm with simulation
