Introduction: This topic tests logical thinking. The key is to correctly identify if events are independent or dependent, as this changes the probabilities in the second stage of a tree diagram. Always check that the probabilities on branches from a single point add up to 1.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Define): What is the difference between an independent event and a dependent event? Give an example of each.

• Prompt 2 (Method): A fair coin is tossed and a fair die is rolled. Draw a grid to show the sample space.

• Prompt 3 (Calculate): From the grid, what is the probability of getting a head and an even number?

• Prompt 4 (Method): A bag contains 3 red and 2 blue balls. A ball is drawn and its colour is noted. Draw the first stage of a tree diagram representing this.

• Prompt 5 (Calculate): The probability of winning a game is 0.4. What is the probability of not winning?

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Task): A bag contains 5 red and 3 blue balls. A ball is drawn, replaced, and a second ball is drawn. Draw a tree diagram showing all probabilities.

• Prompt 2 (Calculate): From the tree diagram, find the probability that both balls are red.

• Prompt 3 (Calculate): Find the probability that at least one ball is blue.

• Prompt 4 (Task): Repeat the experiment from prompt 1, but this time the first ball is not replaced. Draw the new tree diagram.

• Prompt 5 (Calculate): Using the new tree diagram, find the probability that the two balls are of different colours.

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Problem Solve): There are 3 white shirts and 4 black shirts in a cupboard. Two shirts are taken out one after the other without replacement. Represent the sample space on a grid and find the probability that at least one shirt is black.

• Prompt 2 (Problem Solve): The probability that student A passes an exam is 32​ and the probability that student B passes is 43​. Find the probability that only one of them passes the exam.

• Prompt 3 (Problem Solve): A box contains 10 light bulbs, 3 of which are defective. Two bulbs are selected one after the other without replacement. What is the probability that both are defective? What is the probability that exactly one is defective?

• Prompt 4 (Explain): A student argues that in the experiment from the previous prompt, the probability of the second bulb being defective is 103​. Explain why this is incorrect.

• Prompt 5 (Application): A weather forecast says the probability of rain on Saturday is 0.7 and on Sunday is 0.4. What is the probability that it rains on at least one of the days?

Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Conditional Probability): In a class of 30 students, 18 are boys and 12 are girls. 10 of the boys and 6 of the girls have black hair. What is the probability that a randomly selected student has black hair, given that the student is a boy?

• Prompt 2 (Challenge): Bag A contains 3 red and 2 white balls. Bag B contains 2 red and 5 white balls. A coin is tossed. If it is heads, a ball is drawn from Bag A. If it is tails, a ball is drawn from Bag B. Find the probability that the ball drawn is red.

• Prompt 3 (Bayes' Theorem Intuition): Using the information from the previous prompt, if a red ball was drawn, what is the probability that it came from Bag A?

• Prompt 4 (Synthesis): Three people (A, B, C) shoot at a target. The probabilities of them hitting are 0.2, 0.3, and 0.4 respectively. They shoot simultaneously. What is the probability that the target is hit at least once?

• Prompt 5 (Problem Solve): A committee of 3 is to be selected from a group of 5 men and 4 women. What is the probability that the committee consists of 2 men and 1 woman?