Question

Probability Question for ACT??
As part of a probability experiment, Elliott is to answer 4 questions. Each question has 3 possible answers, only 1 of which is correct. If Elliott randomly and independently answers each question, what is the probability that he will answer the 4 questions correctly?
The answer is 1/81 but how?

Answer 1

The odds of getting the first question answered correctly is \(\large\rm \dfrac{1}{3}\).

The odds stay the same for each successive question.
He wants to get all 4 of these correct and they are independent events so the multiplication principle tells us to multiply all these odds together if we want all events to happen.\[\large\rm \frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3}=\frac{1}{3^4}=\frac{1}{81}\]

Answer 2

Understand how that works? :O