I came up with a question several hours ago when I was checking out the 2016 OMO exam. I couldn't solve it using OMO's solution. So here is the question: You have 7 (or n) seeds and you plant them all at the same time. One seed grows one day with probability 1/13 independently. When it has grown survives two days. After that probability that the plant dies one day is 1/17. How many days after the planting day is the biggest number of plants alive (expected value). The planting day is the first day and therefore on day one seeds can grow.
I know that there are seven seeds. In addition, I know the following probabilities P(seed->plant)=1/13 and P(plant->dead plant)=1/17. We want to figure out E(most of the plants are alive). Then I don't know who to proceed.
Thank you.