Question

on a 7 - question multiple - choice test, where each question has 3 answers, what would be the probability of getting at least one question wrong? give your answer as a fraction

Explanation:

Step1: Find probability of getting all right

The probability of getting one question right is $\frac{1}{3}$. Since there are 7 independent questions, the probability of getting all 7 questions right is $(\frac{1}{3})^7=\frac{1}{2187}$ using the multiplication - rule for independent events.

Step2: Find probability of getting at least one wrong

The probability of getting at least one question wrong is the complement of getting all questions right. Let $P(X\geq1)$ be the probability of getting at least one question wrong and $P(X = 7)$ be the probability of getting all 7 questions right. Then $P(X\geq1)=1 - P(X = 7)$.
So $P(X\geq1)=1-\frac{1}{2187}=\frac{2187 - 1}{2187}=\frac{2186}{2187}$.

Answer:

$\frac{2186}{2187}$