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 I. Basic math.
 1 Conditional probability.
 A. Definition of conditional probability.
 B. A bomb on a plane.
 C. Dealing a pair in the "hold' em" poker.
 D. Monty-Hall problem.
 E. Two headed coin drawn from a bin of fair coins.
 F. Randomly unfair coin.
 G. Recursive Bayesian calculation.
 H. Birthday problem.
 I. Backward induction.
 J. Conditional expectation. Filtration. Flow of information. Stopping time.
 2 Normal distribution.
 3 Brownian motion.
 4 Poisson process.
 5 Ito integral.
 6 Ito calculus.
 7 Change of measure.
 8 Girsanov's theorem.
 9 Forward Kolmogorov's equation.
 10 Backward Kolmogorov's equation.
 11 Optimal control, Bellman equation, Dynamic programming.
 II. Pricing and Hedging.
 III. Explicit techniques.
 IV. Data Analysis.
 V. Implementation tools.
 VI. Basic Math II.
 VII. Implementation tools II.
 VIII. Bibliography
 Notation. Index. Contents.

## A bomb on a plane.

e are given the probability that one in a thousand passengers on a plane has a bomb. Assuming that the probability to have a bomb is evenly distributed among the passengers, the probability that two passengers have a bomb is roughly equal to . Therefore, I take a bomb on a plane to decrease chances that somebody else has a bomb. What exactly is wrong with this argument?

If I have a bomb then the probability that somebody else has it is the conditional probability by ( Bayes formula ) by independence Similarly, if I decide not to bring a bomb then I am facing the probability Therefore, I don't accomplish anything by bringing a bomb on a plane.

 Notation. Index. Contents.