1. The theoretical driving test currently consists of 50 questions, each with 4 options, of which only one answer is correct. To pass, at least 41 questions must be answered correctly. Johnny goes to the exam unprepared and guesses the answer to every question. a. What is the probability of Johnny giving exactly 11 correct answers? b. What is the probability of Johnny giving at most 7 correct answers? c. What is the probability of Johnny giving less than 10 correct answers? d. What is the probability that Johnny passes on the exam? e. Calculate the probability that Johnny answers at least 5 and at most 15 questions correctly. f. Determine the expectation and the standard deviation of the number of questions that are correctly answered by Johnny.

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