Statistics question - probability (it is long but help on even just 1 question would be grateful)?

A fairground game involves trying to hit a moving target with a gun. A round consists of up to 3 shots. ten points are scored for a hit target, but the round is over if the player misses. Linda has a constant probability of 0.6 of hitting the target and shots are independant of one another.





a) Find the probability that Linda scores 30 points in a round





The random variable X is the number of points Linda scores in a round





b) Find the probability distribution of X





c) Find the mean and the stnadard deviation of X





A game consists of 2 rounds





d) Find the probability that Linda scores more points in round 2 than in round 1

Statistics question - probability (it is long but help on even just 1 question would be grateful)?
a) and b) Every shot Linda scores ten points and continues (60%) or zero points and stops (40%)


Therefore:


after shot 1: 0.6 10 points ;0.4 0 points


after shot 2: 0.6*0.6 20 points ;0.6*0.4=0.24 10 points


after shot 3: 0.6*0.6*0.6=0.216 30 points ;0.6*0.6*0.4=0.144 20 points





c) d) Easy from the input above