Question

the probability that an event will happen is \\(p(e) = \frac{36}{41}\\). find the probability that the event will not happen.

the probability that the event will not happen is \\(\square\\).
(type an integer or a simplified fraction.)

Explanation:

Identify the given probability

Using the Probability Axioms knowledge point

$$ P(E) = \frac{36}{41} $$

Apply the complement rule

The probability of the complement event \(E'\) (the event not happening) is:

$$ P(E') = 1 - P(E) $$

Calculate the complement probability

$$ P(E') = 1 - \frac{36}{41} = \frac{41}{41} - \frac{36}{41} = \frac{5}{41} $$

Answer:

The probability that the event will not happen is <blank>\(\frac{5}{41}\)</blank>.
(Type an integer or a simplified fraction.)