29
– Probability

1. In how many ways can we
select a set of four capacitors from a shipment of 100?

2. If two capacitors in the shipment of
100 are known to be defective, how many ways can we select a set of four
non-defective capacitors?

3. If two capacitors in the shipment of
100 are known to be defective, how many ways can we select a set of four
capacitors such that at least one is defective?

4. If two capacitors in the shipment of 100
are known to be defective, what is the *probability*
of selecting four capacitors with at least one defective unit?

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5. A card is selected from an ordinary 52
card desk. What is the probability that the card is the ace of spades?

6. A card is selected from an ordinary 52
card desk. What is the probability that the card is a jack?

7. Two fair dice are rolled. What is the
probability that the sum of the number on the dice is odd?

8. Two fair dice are rolled. What is the
probability that the sum of the numbers on the dice is 9?

(You may wish to consider
verification by exhaustion.)

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For
exercises 9-12, an unprepared student takes a 10-question true-false quiz and
guesses at the answer to every question.

9. What is the probability that the
student answers every question *correctly*?

10. What is the probability that the student
answers every question *incorrectly*?

11. What is the probability that the student
answers *exactly one *question
correctly?

12. What is the probability that the student
answers *exactly five* questions
correctly?