Answer to Question #330455 in Statistics and Probability for Kido

Question

n a game of gambling a player tossesa fair coin. Ifit falls head,he wins 100 cedis and if it

falls tail he loss 100 cedis. Aplayer with 800 cedis tossesthe coin six times. What is the

probability that he will be left with 600 cedis?

Answer 1

The coin is fair, the probability that it falls head $p=0.5,$ the probability that it falls tail $q =1-p=1-0.5=0.5.$

Let the player gets $n$ heads and $(6-n)$ tails,

$100\cdot n-100\cdot(6-n)=600-800,\\ 200n=400, n=2.$

So, we need to find the probability of getting 2 heads and 4 tails.

We have a Bernoulli trial,

$P(X=2)=\begin{pmatrix}6\\2\end{pmatrix}\cdot p^2\cdot q^{6-2}=\\ =\cfrac{6!}{2!\cdot(6-2)!}\cdot 0.5^2\cdot 0.5^4=0.2344.$