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2 answers:
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Answer:
(1a) 9.54e-07 (1b) 0.9437 (2)
Step-by-step explanation:
We have n = 10 questions. For each question in the multiple choice exam, we can choose the correct answer with probability p = 0.25 or an incorrect answer with probability q = 0.75 (just by guessing). Besides is reasonable to believe that questions are independent. Let X be the random variable that represents the number of correct answers (just by guessing) observed during the n = 10 questions, so, X have a binomial distribution.
(a) The probability of getting a perfect score just by guessing is
(b) The probability of getting at least one question correct, just by guessing
2. Each RUID is 9-digits long, there are 10 digits, each of the nine positions for a digit of the RUID has 10 posibilities except the 4th and 5th positions which must be both 0. For the multiplication rule there can be different RUIDS.