Grade 7 Probability: Compound Events

Multiple events together

What You'll Learn

Count the outcomes of two independent events
Multiply for "and then", add separate outcomes

📖Compound

Two picks with replacement (or two spins) are independent: P(A and then B) = P(A) × P(B). Two picks from 10 marbles have 10 × 10 = 100 equally likely outcomes. For "the same color both times", find each color's chance and add them.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
A bag has 3 yellow, 2 blue and 2 red marbles. You pick a marble, put it back, and pick again. What is the probability of picking the same color both times?
1. The marble goes back in the bag, so the first pick does not change the second — the two picks are independent. There are 7 marbles, so two picks have 7 × 7 = 49 equally likely outcomes.
2. "Same color" means yellow both times OR blue both times OR red both times. Multiply for each: P(yellow, yellow) = 3/7 × 3/7 = 9/49; P(blue, blue) = 2/7 × 2/7 = 4/49; P(red, red) = 2/7 × 2/7 = 4/49.
3. These can't happen together, so add them: 9/49 + 4/49 + 4/49 = 17/49.
Answer: 17/49
Example 2
A bag has 4 red and 4 blue marbles. You pick a marble, put it back, and pick again. What is the probability of picking red both times?
1. The marble goes back in the bag, so the first pick does not change the second — the two picks are independent. There are 8 marbles, so two picks have 8 × 8 = 64 equally likely outcomes.
2. P(red) = 4/8 each time.
3. Multiply: 4/8 × 4/8 = 16/64, which simplifies to 1/4.
Answer: 1/4
Example 3
A spinner has 9 equal sections: 2 red, 5 blue and 2 green. You spin it twice. What is the probability of spinning green first and then red?
1. The first spin does not change the second — the two spins are independent. There are 9 equal sections, so two spins have 9 × 9 = 81 equally likely outcomes.
2. P(green) = 2/9 and P(red) = 2/9.
3. Multiply for "and then": 2/9 × 2/9 = 4/81.
Answer: 4/81