Waste less time on Facebook — follow Brilliant.

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, 4 months ago

No vote yet
2 votes


Sort by:

Top Newest

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, 4 months ago

Log in to reply

20 Akhil Kumar · 1 year, 5 months ago

Log in to reply

pls check for the soln on the following link www.careerpoint.ac.in Sumedh Bang · 3 years, 4 months ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...