Conditional Coin Probability

P(B|A) with coin flip examples

P(Sequence HHT | Exactly 2 Heads in 3 Flips)

Question

You flip three coins and are told there are exactly 2 Heads. What is the probability that the sequence was specifically HHT?

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

The reduced sample space (exactly 2 Heads):

HHT

HTH

THH

Among outcomes with exactly 2 Heads, how many are HHT?

Answer

All three sequences with exactly 2 Heads are equally likely:

HHT

P = 1/3

HTH

P = 1/3

THH

P = 1/3

Each arrangement of 2 Heads among 3 positions is equally likely, so each has probability 1/3.