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Probability Problem

This appeared in K.V.P.Y. 2012... Please help.

A man tosses a coin \(10\) times, scoring \(1\) point for each head and \(2\) points for each tail. Let \(P(k)\) be the probability of scoring at least \(k\) points.

Find the largest value of \(k\) such that \(P(k)>\frac{1}{2}\)

Note by Krishna Jha
3 years, 1 month ago

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We can make use of a generating function to get the number of ways to score points:

\(G(z) = (z^1+z^2)^{10}\)

The coefficient of each \(z^i\) for i=10..20 is the number of ways of scoring 'i' points.

We can see that the largest k occurs in the middle of the expansion, which is k=15

\(P(k=15) = \dfrac{\sum_{i=5}^{10}\binom{10}{i}}{2^{10}}=\frac{638}{1024}=0.623046875\) Gopinath No · 3 years, 1 month ago

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20 Akhil Kumar · 1 year, 2 months ago

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pls check for the soln on the following link www.careerpoint.ac.in Sumedh Bang · 3 years, 1 month ago

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