A test consists of 10 multiple-choice questions. Assume that a test taker random

Question

A test consists of 10 multiple-choice questions. Assume that a test taker randomly guesses a choice for each and every question, and assume that each question is equally likely to be guessed correctly (C) or wrong (W). 1. Clearly explain in plain English the meaning of outcome CWWWCWCCWW, and determine the total number N of the outcomes in the sample S. 2. Let A be the event that the test taker may only guess evenly numbered questions correctly. Determine N(A) by explicitly listing all the outcomes in A, and P(A).

Explanation / Answer

1. The test taker answered 4 questions correct and 6 wrong, in that order. The total number of possible outcomes would be 2^10 = 1024. Depending on how many questions are on the test, the number of outcomes would be N = 2^S. 2. WCWCWCWCWC. N(A) =1. P(A) = 0.5^10 = 0.0009765625

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