# 2022 Probability Methods Exam

Can someone pls show me the full working out for this question? I did not understand how to form the equation to solve for the unknown value on the tree diagram

I will add the first part of the question as information there is relevant to yours:

It should be easy to draw a probability tree based on this information. The part above just adds another level to the probability tree - students saving or not saving water.

Two key pieces of information were given in the question:

• Students who were concerned about water shortages (W) were twice as likely to save water (S) than those who were not concerned about water shortages (W’). We will then assign x to the probability that a student from the group that was not concerned about water shortages (W’) saved water (S) and 1-x to the probability that a student from the group W’ didn’t save water (S’). Then I will assign 2x to the probability that a student from the group which is concerned about water shortages (W) saved water (S) and 1-2x to the probability that a student from the group W didn’t save water (S’).

• Concern over climate change didn’t effect probability of students saving water, so we will assign the same x, 1-x, 2x, and 1-2x to the group which was not concerned about climate change.

Now we can create an equation adding all probabilities that a student saved water:

0.7 (0.85 * 2x +0.15x) + 0.3(0.55 * 2x + 0.45x) = 0.5632

Solving the equation for x we will have x = 0.32