#33 Top 50 Mistake

⚠️ Subtracting the wrong value for complementary events

"The Complement Confusion"

Probability & Statistics

The Mistake in Action

P(rain) = 0.3. Find P(no rain).

Student writes: "P(no rain) = 0.3 − 1 = −0.7"

🧠 Why It Happens

Students know that complementary events involve subtraction but subtract in the wrong order, giving a negative probability (which is impossible).

The Fix

The complement formula is: $$P(\text{not } A) = 1 - P(A)$$

It's always 1 minus the probability, never the other way around.

$P(\text{no rain}) = 1 - 0.3 = 0.7$

Check: Negative probability? Impossible! Go back and fix it.

🔍 Spot the Mistake

Can you identify where this student went wrong?

P(rain) = 0.3

P(no rain) = 0.3 − 1 = −0.7

Click on the line that contains the error.

📚 Related Topics

Learn more about the underlying maths: