Question

a student takes a six - question multiple choice (a, b, c, d) quiz. assuming that no questions are left unanswered, in how many different ways can the the questions be answered? find the probability of randomly guessing the answer to all six questions correctly. round your answer to four decimal places.

Explanation:

Step1: Calculate the number of ways to answer the quiz

Each question has 4 choices. By the multiplication principle, for \(n = 6\) questions, the number of ways to answer is \(4\times4\times\cdots\times4=4^{6}\).

$$4^{6}=4096$$

Step2: Calculate the probability of guessing all correct

The probability of getting one question correct by guessing is \(\frac{1}{4}\). Since the questions are independent, the probability of getting all 6 correct is \((\frac{1}{4})^{6}\).

$$(\frac{1}{4})^{6}=\frac{1}{4096}\approx0.00024414$$

Rounding to four decimal places gives \(0.0002\).

Answer:

The number of ways to answer the questions: \(4096\)
The probability of guessing all correct: \(0.0002\)