Math CentralQuandaries & Queries


Question from Tanja, a teacher:
A biased coin where P(heads) =3/5 is flipped 4 times.
What is the probability of getting at least 3 heads given at least 1 heads is flipped?
I can calculate this using P(A|B) =P(AandB)/P(B) but I've had students asking me how you would work this question out the "long way"
without the formula. I'm am unsure about how you do this the long way.

Well, if you want the long way...

Use a probability tree to assign probabilities to each of the 16
outcomes. Cross out outcomes without at least one head. Add probabilities to find what proportion of the restricted sample space has at least 3 heads.

Good Hunting!

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