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It's simple. Just use Bayes' theorem.The probability she likes you is[math]P(like|smile) = \frac{P(smile|like)P(like)}{P(smile)}[/math][math]P(like|smile)[/math] is what you want to know - the probability she likes you given the fact that she smiles at you.[math]P(smile|like)[/math] is the probability that she will smile given that she sees someone she likes.[math]P(like)[/math] is the probability that she likes a random person.[math]P(smile)[/math] is the probability that she will smile at a random person.For example, suppose she just smiles at everyone. Then intuition says that fact that she smiles at you doesn't mean anything one way or another. Indeed, [math]P(smile|like) = 1[/math] and [math]P(smile)=1[/math], and we have[math]P(like|smile) = P(like)[/math]meaning that knowing that she smiles at you doesn't change anything.At the other extreme, suppose she smiles at everyone she likes, and only those she likes. Then [math]P(smile) = P(like)[/math] and [math]P(smile|like) = 1[/math]. Then we have[math]P(like|smile) = 1[/math]and she is certain to like you.In the intermediate case, what you need to do is find the ratio of odds of smiling at people she likes to smiles in general, multiply by the percentage of people she likes, and there is your answer.The more she smiles in general, the lower the chance she likes you. The more she smiles at people she likes, the better the chance. And of course the more people she likes, the better your chances are.Of course, how to actually determine these values is a mystery I have never solved.

The answer is obviously 781. Consider the polynomial[math]\displaystyle P(X) = \frac{27 X^4}{8}-\frac{117 X^3}{4}+\frac{765 X^2}{8}-\frac{519 X}{4}+61. \tag*{}[/math]It is easily checked that[math]\begin{align*} P(1) &= 1 \\ P(2) &= 4 \\ P(3) &= 16 \\ P(4) &= 64 \\ P(5) &= 256. \end{align*} \tag*{}[/math]And, of course, [math]P(6)[/math], which clearly should be the next term in the sequence, is 781.

As you sow, so shall you reap!In 2010,P Chidambaram to Amit Shah : You will not be able to withstand the storm that I am going to bring to your life!In 2019,Amit Shah to P Chidambaram : I am the storm!What a “coincidence”!!In 2010, when P Chidambaram was Home Minister in Congress-led government, Amit Shah was arrested by CBI for murder in Sohrabuddin case in Gujarat, which was alleged fake.P Chidambaram ordered to arrest Amit Shah on murder charges.According to the case, Amit Shah, then home minister of Gujarat ordered the extra judicial killings of Sohrabuddin, his wife and their friend who was witness to Sohrabuddin's killing in 2005.Amit Shah was later granted clean chit by the Supreme Court as the court found no involvement of Mr. Shah in the case.And now, in 2019, the Supreme Court has rejected P Chidambaram's request for protection from arrest and has ordered to cancel his bail request after corruption case was filed against him.Former Home Minister P Chidambaram and his son holds huge assets in more than 12 countries across the world.The Income Tax Chennai Investigation Department has submitted a report of 200 pages of assets of the former Home Minister P Chidambaram after which he went missing for several hours before getting arrested.On the contrary, now Home Minister Amit Shah who was arrested on murder charges back in 2010 by the CBI, co-operated with the officials and himself surrendered in the CBI office, after holding the press conference stating he will come out clean and he did.Sushmita's answer to Do you think P. Chidambaram's arrest is intentional by Modi and Amit Shah?Edit : I am not blindly supporting any party over here.Corruption is corruption and it needs punishment, be it Congress, BJP or any other party!Peace!