suppose you are taking a multiple choice quiz that EX 5. Suppose that you are ta
ID: 3049299 • Letter: S
Question
suppose you are taking a multiple choice quiz that EX 5. Suppose that you are taking a multiple-choice quiz that consists of six questions. Each question has four possible answers, only one of which is correct. To complete the quiz, you randomly guess the answer to each question. Hw A. What is the probability of guessing the first two questions correctly? B. What is the probability of guessing the first two question correctly and the rest of the four questions incorrectly? C. What is the probability of guessing exactly two an D. What is the probability of guessing at most one ansver correctly? E. What is the probability of guessing more than one answer correctly F. What is the probability of guessing at least one of the questions correctly?Explanation / Answer
n = 6
P(correct answer) = 0.25
A) Probability = 0.25 * 0.25 = 0.0625
B) Probability = (0.25)^2 * (0.75)^4 = 0.0198
C) P(X = 2) = 6C2 * (0.25)^2 * (0.75)^4 = 0.2966
D) P(X < 1) = P (X = 0) + P (X = 1)
= 6C0 * (0.25)^0 * (0.75)^6 + 6C1 * (0.25)^1 * (0.75)^5 = 0.5339
E) P(X > 1) = 1 - P(X < 1)
= 1 - 0.5339
= 0.4661
F) P(X > 1) = 1 - P (X < 1)
= 1 - P(X = 0)
= 1 - (6C0 * (0.25)^0 * (0.75)^6)
= 1 - 0.178
= 0.822
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