**Non-Coding Problem**:

Given a bag of n balls each with a different color. Each time you pick up a pair of balls and paint both to one of their colors. What's the expected number of steps before all balls become the same color?

**Analysis**:

This is a problem from the "Green Cover Book". It's easy to see that we have the following transition probability. Thus if we let \(\mu_i\) be the expected number of steps getting to one color when the bag has i distinct colors, then we have \[ \mu_i = 1 + \frac{i(i-1)}{n(n-1)} \mu_{i-1}+\left(1-\frac{i(i-1)}{n(n-1)}\right) \mu_i. \] From this we can use induction to prove that \[ \mu_i = \frac{i-1}{i} n(n-1). \] Therefore we have \[ \mu_n = (n-1)^2. \]

## 3 comments:

The main focus will be on learning different techniques in solving word problems.Once the techniques are in place, solving word problems would be a breeze.

psle primary 4 math tuition

psle primary 3 math tuition

psle primary 6 science tuition

psle primary 5 science tuition

psle primary 4 science tuition

psle primary 3 science tuition

best math tuition

primary mathematics tuition

Online PSLE tuition helps student to Ace their PSLE Exams Easily

online PSLE tuition

Primary PSLE Tuition online

PSLE tuition Singapore

PSLE tuition

psle math tuition online

psle english tuition online

psle science tuition online

psle english tuition singapore

online english tuition singapore

Every course is taught by the best teachers and conducted in an engaging manner to keep students involved.

maths tuition singapore

english tuition singapore

science tuition singapore

maths tuition

english tuition

science tuition

best psle science tuition

best science tuition

Post a Comment