362 Frequently Asked Questions In Quantitative Finance
Probability
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0.005
0.01
0.015
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0.025
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0.035
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Number ahead of you in queue
Biased coins
You havenbiased coins with thekth coin having
probability 1/(2k+1) of coming up heads. What is the
probability of getting an odd number of heads in total?
(Thanks to FV.)
Solution
I include this as a classic example of the induction
method. Usepnto denote the required probability.
Aftern−1 tosses there is a probabilitypn− 1 that there
have been an odd number of heads. And therefore a
probability of 1−pn− 1 of there having been an even
number of heads. To get the probability of an even
number of heads after another toss,nin total, you mul-
tiply the probability of an odd number so far by the
