Calculating Probability

A mug on your desk holds 10 identical looking pens, three of which do not work. If you select three pens at random, what is the probability that at least one of the pens you selected works? In this problem, you will calculate the probability two different ways (directly and also using the complement) and then compare the two methods. HINT: When you see words like "at least" so many or "at most" so many, it means you should start my making a list of the possible cases so that you don't leave anything out. Calculating the probability directly: A.) Which of the cases (outcomes) listed above in the hint are included in the event of at least one of the three pens working? B.) Find the probability of the event by adding up the probabilities of the outcomes. Calculating the probability using the complement: C.) How are P(E') and P(E) related? Write down the formula. Explain why it is true. D.) Which of the outcomes listed above in the hint are included in the complement of the event? E.) Find the probability of the complement of the event. Then use the formula from C.) to find the probability of the event (the probability of at least one selected pen working). F.) Which one of the two methods for find the probability of this event (involving the words "at least") did you prefer? Why?

Those are excellent hints. I suggest you use them.

Let's see what you get.