A rocket is launched from the Earth. Random forces cause the rocket to move left and right. In an interval of time t, the rocket is moved according to a log-normal distribution N(t), where it is equally likely to be moved left or right. There is an asteroid belt on the right side X miles away.

1. What is the probability that the rocket will move j miles to the left in n*t (where j<x)?2. What is the probability that the rocket will hit the asteroid belt and explode?3. What is the probability that the rocket will move into the danger zone (beginning at y miles less

than x) and then return to safety? And what is the probability that the rocket will move into the danger zone and then return to safety z times?

These are difficult problems. Feel free to assign values to each variable to help you solve the problem, but answer in a generalized form.

Hint: Summing probabilities that aren’t mutually exclusive are found by summing them as if they were mutually exclusive and then subtracting their “overlap”.

95% of the time, I will be+/- x number of pennies, if I gain/lose a penny every time I flip a coin and guess heads or tails correctly/incorrectly……? This would be the worst case position at a worst case run scenario (i.e. 10 hands down +15 hand lose streak=bring 25 hands worth of money to casino)