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# True or False Questions & Probability

1. True or false, and explain:

(a) If something has probability 1,000%, it is sure to happen.
(b) If something has probability 90%, it can be expected to happen about nine times as often as its opposite.

2. The chance of A is 1/3; the chance of B is 1/10. True or false, and explain:

(a) If A and B are independent, they must also be mutually exclusive.
(b) If A and B are mutually exclusive, they cannot be independent.

3. Three cards are dealt from a well-shuffled deck.

(a) Find the chance that all of the cards are diamonds.
(b) Find the chance that none of the cards are diamonds.
(c) Find the chance that the cards are not all diamonds.

4. A die will be rolled 6 times. What is the chance of obtaining exactly 1 ace?

5. A die will be rolled 10 times. The chance it never lands six can be found by one of the following calculations. Which one, and why?

6. True or false: if a coin is tossed 100 times, it is not likely that the number of heads will be exactly 50, but it is likely that the percentage of heads will be exactly 50%. Explain

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1. True or false, and explain:
(a) If something has probability 1,000%, it is sure to happen.
Answer: Nothing can have probability 1000 percent -- probability values are restricted to zero to one, or to zero percent to 100 percent. Note that 1.00 = 100 percent, just as one dollar = 100 cents.

(b) If something has probability 90%, it can be expected to happen about nine times as often as its opposite.
Answer: If something has probability 90 percent, it can be expected to happen about nine times as often as its opposite. Depends on whether "something" and "its opposite" are the only alternatives -- if they are mutually exclusive and collectively exhaustive, then yes, at least as the expected value of a sequence of random trials.