The Problem:

Question

Zared plays basketball on his high school team. One of the things he needs to practice is his free throws. On his first shot, there is a probability of 0.6 that he will make the basket. If he makes a basket, his confidence grows and the probability he makes the next shot increases by 0.05. If he misses the shot, the probability he makes the next one decreases by 0.05.

He takes 5 shots. What is the probability he makes at least 3 shots? (Hint: a tree diagram might be a helpful strategy)

3 marks for showing possible outcomes
5 marks for showing work
1 mark for a correct strategy to find final probability
1 mark for correct final probability