# Question 2The probability of getting a multiple choice question wrong is 0.8. A weekly quiz has 10multiple choice questions. Assume independence between the questionsa)What is the probability of getting 5 questions correct?b)What is the probability of getting 5 questions wrong?c)What is the probability of getting at least 8 questions correct?d)What is the probability of getting more than 8 questions correct?e)What is the probability that you will get a zero in the quiz?

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66 views help_outlineImage TranscriptioncloseQuestion 2 The probability of getting a multiple choice question wrong is 0.8. A weekly quiz has 10 multiple choice questions. Assume independence between the questions a) What is the probability of getting 5 questions correct? b) What is the probability of getting 5 questions wrong? c) What is the probability of getting at least 8 questions correct? d) What is the probability of getting more than 8 questions correct? e) What is the probability that you will get a zero in the quiz? fullscreen
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Step 1

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Step 2

Introduction:

If X ~ Bin (n, p), then the probability mass function of X is:

p (x) = (nCx) px (1 – p)nx; for x = 0, 1, …, n; 0 < p <1; p (x) is 0 otherwise.

Here, number of trials is the number of questions in the weekly quiz, n = 10.

Step 3

Part a:

Consider the event of getting a question correct as a success.

In the quiz, P (getting a question wrong) = 0.8.

The remaining probability must be the probability of getting the question correct. Thus, P (getting a question correct) = 0.2 (= 1 – 0.8).

Thus, the probability of success is, p = 0.2.

Denote X as the number of correct answers, that is, the number of successes in n = 10 trials.

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