Grade 7 Skill Standards: CCSS 7.SP.C.8
Probability of Compound (Independent) Events (Grade 7)
Two events are independent if one doesn't affect the other (like two separate coin flips).
What it is
Understanding probability of compound events
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.
Worked Example
Seeing it in action
1
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.
Visual model
Two independent die rolls multiply: 1/6 × 1/6.
Watch for this
A common mistake, and the fix
Adding the probabilities when both events must happen.
Two 6s in a row is 1/6 × 1/6 = 1/36, not 1/6 + 1/6 = 2/6. Needing both events makes the chance smaller, not bigger.
Interactive Check
Try a few
Two coins, P(both heads)?
Answer: 1/4
P(heads and rolling a 3)?
Answer: 1/12
1/2 × 1/6.
Spinner P(gold)=1/2 twice, P(both gold)?
Answer: 1/4
½ × ½.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
More Free Practice
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