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fomenos
2 years ago
7

A multiple choice test has two parts. There are 4^12 ways to answer the 12 questions in Part A. There are 4^5 ways to answer the

5 questions on part B. How many ways are there to answer all 17 questions? If you guess each answer, what is the probability you will get them all right
Mathematics
1 answer:
LiRa [457]2 years ago
8 0

Using the Fundamental Counting Theorem and the probability concept, it is found that:

  • There are 4^{17} ways to answer all 17 questions.
  • 4^{-17} probability you will get them all right.

<h3>What is the Fundamental Counting Theorem?</h3>
  • It is a theorem that states that if there are n things, each with n_1, n_2, \cdots, n_n ways to be done, each thing independent of the other, the number of ways they can be done is:

N = n_1 \times n_2 \times \cdots \times n_n

<h3>What is a probability?</h3>
  • A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

  • The questions in part A and in part B are independent.
  • For the 12 questions in part A, there are 4^{12} ways to answer, hence n_1 = 4^{12}.
  • For the 5 questions in part B, there are 4^{5} ways to answer, hence n_2 = 4^{5}.

Then:

N = n_1 \times n_2 = 4^{12} \times 4^5 = 4^{17}

There are 4^{17} ways to answer all 17 questions.

Only one outcome in which all the guesses are correct, hence:

p = \frac{1}{4^{17}} = 4^{-17} probability you will get them all right.

You can learn more about the Fundamental Counting Theorem at brainly.com/question/24314866

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