A hint to get started
Respect the first-miss stopping rule before comparing rounds
A fairground game involves shooting at a moving target. A round has a maximum of 3 shots and ends immediately after a miss. Each hit scores 10 points. Linda hits with probability 0.6 on each shot, and all shots taken are independent.
(i) Find the probability that she scores 30 points in a round. marks
X is her score in one round.
(ii) Find its distribution. marks
(iii) Find its mean and variance. marks
(iv) A game consists of two rounds. Find the probability that she scores more in round 2 than round 1. marks
[2017/SAJC/II/8]
CJC · Review problems · Question 8
Enumerate the stopped paths; not every round contains three shots.