#33
Top 50 Mistake
Subtracting the wrong value for complementary events
"The Complement Confusion"
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: