Grade 10: Probability

Warm up with a few quick probability warm-ups on the board while the class settles, so every child starts thinking about the skill.

Compound probability covers situations with more than one event at once: complementary events (an event and its opposite, adding to 1), independent events combined with 'AND' (multiply), and conditional probability (the chance of one event given another has already happened). Model the method clearly, thinking aloud:

• Start with complementary events: P(A) and P(not A) always add to 1, so one can always be found from the other.
• Teach independent 'AND' events by multiplying the individual probabilities, listing the full sample space for a small example first (e.g. all 12 coin-and-die outcomes).
• Introduce two-way tables for organising combinations of two categories, checking the four cells always sum to the total.
• For conditional probability, show that removing an item without replacement changes the probabilities for what happens next.
• Compare a simulation's relative frequency (from repeated trials) with the theoretical probability, discussing why small differences are expected chance variation.

Work this through step by step on the board, then have the class talk you through a second one.

• A coin is flipped and a 6-sided die is rolled
• P(heads AND rolling a 4) = P(heads) x P(rolling a 4)
• = 1/2 x 1/6 = 1/12

Do the first few questions of the practice worksheet together, one child explaining each step. Check for understanding before releasing the class to work alone.

Students complete the practice worksheet independently while you circulate and support.

Circulate and look for these, they are the usual sticking points:

• Adding probabilities for 'AND' events instead of multiplying (addition is for 'OR', a different rule).
• Assuming P(A) + P(not A) = 1 only applies to 'fair' events like coins, when it applies to any event.
• Assuming a simulation result different from the theoretical probability means the simulation was done wrong.
• Forgetting that removing an item without replacement changes the probabilities for the next draw.

Pull the class back together. Ask one child to explain probability in their own words, pose a single check question everyone answers on a mini whiteboard, and name what you will build on next lesson.

Use the independent worksheet as the evidence. A child who can complete it accurately and explain one answer has met the objective; anyone who cannot needs the easier level and a short reteach next session.