Welcome to the article A junk drawer at home contains nine pens five of which work What is the probability that you randomly grab three pens from the drawer. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
Final answer:
To find the probability of not ending up with a pen that works when randomly grabbing three pens from the drawer, multiply the probabilities of each event happening.
Explanation:
To find the probability of randomly grabbing three pens from the drawer and not ending up with a pen that works, we need to calculate the probability of each event happening and then multiply them together.
First, the probability of not getting a working pen on the first draw is 4/9 (since there are 4 pens that don't work out of 9 total).
Next, the probability of not getting a working pen on the second draw (assuming we didn't replace the first pen) is 3/8 (since there are only 3 pens that don't work left out of 8 total).
Finally, the probability of not getting a working pen on the third draw (assuming we didn't replace the second pen) is 2/7 (since there are only 2 pens that don't work left out of 7 total).
To find the overall probability, we multiply these probabilities together: 4/9 * 3/8 * 2/7 = 24/504 = 1/21 (rounded to the nearest millionth, this is approximately 0.047619).
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