Questions: The probability that a randomly selected student passes the AP exam is 0.67 . What is the probability of the complement of this event?

Transcript text: The probability that a randomly selected student passes the AP exam is 0.67 . What is the probability of the complement of this event?

Solution

Solution Steps

Step 1: Understand the Complement of an Event

The complement of an event \( A \), denoted as \( A^C \), represents all outcomes where the event \( A \) does not occur. In probability terms, the sum of the probability of an event and its complement is always 1: \[ P(A) + P(A^C) = 1 \]

Step 2: Substitute the Given Probability

Given that the probability of a student passing the AP exam is \( P(A) = 0.67 \), substitute this value into the equation: \[ 0.67 + P(A^C) = 1 \]

Step 3: Solve for the Complement Probability

Subtract \( 0.67 \) from both sides of the equation to solve for \( P(A^C) \): \[ P(A^C) = 1 - 0.67 \] \[ P(A^C) = 0.33 \]

The probability of the complement event is \( 0.33 \).