Explain why an empirical probability, an observed proportion, and a relative frequency are actually three different names for the same thing.
Q. 2One single-digit number is to be selected randomly. List the sample space.
Q. 3If the odds in favor of an event A are 2 to 3, what is the probability that event A will not occur?
Q. 4If the odds in favor of an event B are x to y, what is the probability that event B will occur?
Q. 5A meteorologist predicts that there will be a measurable amount of precipitation or no precipitation on a given day. The sample space is S = precipitation, no precipitation. Event A is defined to be A = precipitation. A student uses P(A) = n(A)/n(S) to obtain P(A) = 0.50 . Explain why this is not correct.
Q. 6A sample space is composed of three outcomes, called A, B, and C. Outcome B is twice as probable as A, and C is twice as probable as B. Find the probabilities of the events of A, B, and C.
Q. 7Amy is interested in determining the probability that a randomly selected card from a standard deck of 52 will be a club. She reasons that the deck contains clubs (C), spades (S), diamonds (D), and hearts (H). She constructs the sample space S = C, S, D, H. Determine if the sample points are equally likely or not equally likely.
Q. 8Heidi is interested in determining the probability that a randomly selected student in her statistics class earned a passing grade (A, B, C, or D) on the first test. She reasons that each student earned either a passing grade (P) or a failing grade (F) and constructs the sample space S = P,F. Are the sample points equally likely or not equally likely?
Q. 9Explain why the following statement is true: if A is an event of a sample space S, then it is possible that P(A) = 1.
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