MathCastle
Statistics & DataSuperchallengeBinomial and Geometric

Binomial and Geometric · Superchallenge problem

A biased coin lands heads with probability 13\dfrac13. Ann tosses it 66 times and Bob tosses it 44 times. Between them they get 55 heads in total. Given this, what is the probability that Ann got exactly 33 of the heads? Express your answer as a common fraction.