Question 16
In-Young generates a string of $B$ zeroes and ones using the following method:
- First, she flips a fair coin. If it lands heads, her first digit will be a $0$, and if it lands tails, her first digit will be a $1$.
- For each subsequent bit, she flips an unfair coin, which lands heads with probability $A$. If the coin lands heads, she writes down the number (zero or one) different from previous digit, while if the coin lands tails, she writes down the previous digit again.
What is the expected value of the number of zeroes in her string?
- First, she flips a fair coin. If it lands heads, her first digit will be a $0$, and if it lands tails, her first digit will be a $1$.
- For each subsequent bit, she flips an unfair coin, which lands heads with probability $A$. If the coin lands heads, she writes down the number (zero or one) different from previous digit, while if the coin lands tails, she writes down the previous digit again.
What is the expected value of the number of zeroes in her string?