“I have a fair coin. When I tossed
it, I got ‘head’ 99 times consistently. What is the probability of getting ‘head’
on the 100th time when I will toss?”
I asked this question to some of the candidates who came for the interview, invariably everyone answered that the probability of getting 'head' on 100th time is .5
One thing is clear that they did
not read the book ‘Black Swan’, because the question was taken from that book. The
other thing that is crystal clear is that they are good at statistics but very naive in dealing with the world of grey. They are just blind to the data provided and
totally trusting the statement that the coin is fair.
On tossing, if a coin turns up ‘head’
for 99 times consistently then how can that be a fair coin? One has to be a
blind believer (another term for a fanatic) to believe that the coin is fair. How
can anyone deny the data? Coincidences take place, but to believe that 99 times
coincidence has taken place is beyond imagination. Yet not a single one noticed
the trap. They took some time and reflected to come up with the answer .5
In the question asked, there are
two parts – one is an assumption and the other is the data. Assumption is that
the coin is fair, and the data is 99 times it has turned up with ‘head’. We believe
the assumption and ignore the data provided. No wonder, any street smart guy is
able to take us for a ride time and again, and we too prefer to live in the
world of ignorance.
Because questioning assumptions
demands not only sharp intelligence but also courage.
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