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Mimi plans to make a random guess at 10 true-or-false questions in a test. A nswer the following questions: (a) Assume random number X is the number...
nswer the following questions:
(a) Assume random number X is the number of correct answers Mimi gets. As we know, X follows a binomial distribution. What is n (the number of trials), p (probability of success in each trial) and q (probability of failure in each trial)?
(b) In order to pass the test, Mimi has to get at least 6 correct answers. What is the probability that she passes the test? (Show work and round the answer to 4 decimal places)
(c) How many correct answers can she expect to get? (Hint : What is the expected value of the binomial distribution?) (Show work)
Assume that you toss a fair six-faced die two times.
4(b) What is the probability that you get a number less than 3 at the first toss? (Show work and write the answer in simplest fraction form)
(c) What is the probability that the product of the two tosses is at most 4? (Show work and write the answer in simplest fraction form)
(d) What is the probability that the product of the two tosses is at most 4, given that you get a number less than 3 in the first toss? (Show work and write the answer in simplest fraction form)
(e) If event A is "Getting a number less than 3 in the first toss" and event B is "The product of two tosses is at most 4". Are event A and event B independent? Use statistical concept and mathematical expression to justify your answer.
