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Which of the following statements are true If a statement
Chapter , Problem 3(choose chapter or problem)
Which of the following statements are true? If a statement is true, prove it. If it is false, give a counterexample. (a) If A is an event with probability 1, then A is the sample space. (b) If B is an event with probability 0, then B = .
Questions & Answers
QUESTION:
Which of the following statements are true? If a statement is true, prove it. If it is false, give a counterexample. (a) If A is an event with probability 1, then A is the sample space. (b) If B is an event with probability 0, then B = .
ANSWER:Step 1 of 2
Given statement is
If A is an event with probability 1, then A is a sample space.
Let us consider a random experiment of coin tossing. Suppose a coin is tossed for one time.
Let A be the event that either head or tail will be obtained. Then,
Thus, it is proved that , but A is not the sample space.
So, the given statement is false.