easy Probability
A release-checked easy problem for training Expected Value, Conditional Expectation.
A bagel factory has a conveyor belt that delivers bagels continuously. Every bagel is either good (G) or bad (B). If a given bagel was G, the next bagel is also G with probability $\dfrac{2}{5}$. If a given bagel was B, the next bagel is also B with probability $\dfrac{3}{5}$. You woke up to find that the first bagel is a bad one. Find the expected number of bagels that pass until another bad bagel.
This Probability problem is tagged Expected Value, Conditional Expectation. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
Probability · Akuna
Probability
Probability
Probability · SIG, DE Shaw
Probability · Jane Street
Probability