Date: 7 Jun 1995 13:59:34 -0400 From: cad 10 Subject: Probability Hi. I am just wondering how probability works. How is it specifically done? Sincerely, Patrick Bettencourt
Date: 7 Jun 1995 15:00:47 -0400 From: Heather Mateyak Subject: Probability Well, I will try to give you a few examples of some probability questions. Probability questions that deal with games are usually most interesting to me. For example, say you're playing with a deck of cards with a friend. Say he challenges you that if you draw an ace on your first pick, he will have to buy you lunch the next day. How good are your chances of winning? Well, this is a probability question. Since there are four aces in 52 cards, your chances of winning are 4/52, or 1/13. So, the probability of you're picking an ace is 1/13, whereas the probability of you not picking an ace is 12/13. The odds are against you, but it isn't completely unlikely. Let's take a more complicated example. Let's say you and your friend are playing with two dice. He gives you the same challenge, except this time, he challenges you to roll two sixes. The probability of rolling a six on each die is 1/6, but how about both at the same time? To figure the probability out here, we have to multiply the probability of getting a six on each die. So, we have 1/6 x 1/6, and our probability for rolling two sixes is 1/36. Your chances are even worse here! Another interesting thing probability can show you that is somewhat practical is your chances of winning the lottery. If you play one of those 3-digit lottery tickets where you have to guess the 3-digit number exactly, your probability of winning is 1/1000. You can figure this out by noting that the probability of you're getting the first number right is 1/10. The probability of getting all three right is then 1/10 x 1/10 x 1/10. Not too good of a chance! The 4-digit number is even harder! Can you guess what the probability of winning that lottery might be? And even more amazing is the tiny probability of winning those multi-million dollar lotteries. That would be a little trickier to figure out, but it is a slightly different problem. Say there are 70 numbers they pick from. Your chances of getting the first number right is 1/70. But since one ball has been removed, your chances of getting the second number right is 1/69. If there are six numbers picked, can you figure out what the probability of winning this lottery is? (Remember to multiply all of the individual probabilities together... 1/70 x 1/69 x ...etc.) The last thing I can tell you is that probability can be used in a lot of more important things than games. One area probability can be utilized is in the area of genetics. A monk, I believe his name was Mendel, realized the use of probability in genetics sometime around 1000a.d. or 1200a.d. I can't exactly remember. Probability in genetics is very interesting, and can help you see once again how useful math can be! Well, I hope this helps. If I confused you anywhere, please write back. This is my first time responding to Dr. Math questions. -Heather
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.