• cassieforlife5
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?
  • schrodinger
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  • zepdrix
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.\[\large\rm \frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3}=\frac{1}{3^4}=\frac{1}{81}\]
  • zepdrix
Understand how that works? :O

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