Probability of Compound (Independent) Events (Grade 7)
Two events are independent if one doesn't affect the other (like two separate coin flips). The probability that both happen is the product of their probabilities: P(A and B) = P(A) × P(B). P(heads then heads) = 1/2 × 1/2 = 1/4.
Understanding probability of compound events
Two events are independent if one doesn't affect the other (like two separate coin flips). The probability that both happen is the product of their probabilities: P(A and B) = P(A) × P(B). P(heads then heads) = 1/2 × 1/2 = 1/4.
Key Idea
Two events are independent if one doesn't affect the other (like two separate coin flips). The probability that both happen is the product of their probabilities: P(A and B) = P(A) × P(B). P(heads then heads) = 1/2 × 1/2 = 1/4.
Seeing it in action
Worked example
P(rolling a 6, then a 6) on a fair die twice?
Each roll: P(6) = 1/6. Independent, so multiply: 1/6 × 1/6 = 1/36.
Two independent die rolls multiply: 1/6 × 1/6.
Try a few
Two coins, P(both heads)?
P(heads and rolling a 3)?
1/2 × 1/6.
Spinner P(gold)=1/2 twice, P(both gold)?
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