Darts Probability
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Darts Probability
can someone please explain the binomial probability distribution to me please?
i have a statistics exam tomorrow and i still dont understand this! i have a past exam paper and a question on binomial probability distribution is: megan throws darts at a target she can hit the target with 7 out of 9 throws. megan throws 3 darts. assuming a binomical distribution, work out the probability that she hits the target exactly twice. you may use (p+q)^3=p^3+3p^2q+3pq^2+q^3
please help if you can!
The binomial distribution (e.g., B(n,p)) is the sum of n independent bernoulli p trials/distributions.
You are throwing the dart 3 times and you want to hit twice exactly, that can happen three ways (hit 1 and 3, 1 and 2, or 2 and 3); and summing that all up can be annoying (especially when you are looking at something with more trials than this. That is where the binomial PDF (probability density function) comes in.
(nCr)*p^r*q^(n-r)
The nCr ( =n!/(r!*(n-r)!)) says how many ways can you pick r from n (in your case; how many different ways can you throw three darts and hit twice).
The remainder (p^r*q^(n-r)) is the probability of any one of those occurring combinations occuring; that is where the independent bernoulli trial part comes in. Since each trial is independent, the order of the events doesnt matter (e.g., p*q*p =p*p*q = q*p*p = p^2*q) .
Thus, so long as you know how many possible combos there are (from the nCr) you just multiply it by the probability of an event.
Given the information you have, you know p is 7/9 (the probability of success). q is usually defined as 1-p, in this case 2/9. n (the number of trials) is 3, and r (the number of successes) is 2. Use the above equation and you can get your answer.
Just as an FYI, your (p+q)^3 bit wont help you much since by definition p+q =1, so (p+q)^n = 1.
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I'm Probability Wrong
Know the Rules and Be an Expert at Darts
There are many theories about how darts originated, and one of the most common is that it had its roots in archery. The dartboard itself may come from a tree cross section, though there's no real proof. Dartboards come in several varieties, with different numbers of segments and different diameters. There are numerous variations on the game of darts, but the most commonly played version is version 501, which is probably what you'll play in your local hangout.
The distance from the floor to the bullseye on a dartboard is 5 feet 8 inches. The distance referred to as the "oche" is the distance between the front of the board and the toe line, and the standard oche is 7 feet, 9.25 inches. Most professional darts matches are called "501 Up," and the rules are simple.
Every player starts with a score of 501. He or she takes turns throwing 3 darts. The score for every turn is added up and deducted from the total. A bullseye gets 50 points, while the outer ring gets 25. A dart in the double ring or treble ring counts for double or triple the score for that segment. The goal is to get the score down to exactly zero, and landing the last dart in the bullseye or in a double segment.
If a player's score goes to 1 or goes below zero, the turn is considered a "bust" and ends, with the player's score returning to what it was before the turn. On a last turn, it is not required that the player throw all three darts: he or she can win with the first or second dart on that turn too.
When a player has mastered his technique enough to be able to develop a strategy, he'll attempt to end up with a score that can be repeatedly cut in half to avoid ending up with a 1 and a bust. It also keeps players from having to throw extra darts just to reduce the score to an even number.
While the rules for darts are fairly simple, learning how to throw darts well takes time and practice. When you learn to throw, your grip on the dart should be stable and firm, but not tense. If the tips of your fingers turn white from squeezing the dart, it's a good sign your grip is too tight. If your muscles are stiff enough that you have a hard time letting go of the dart, you won't throw well. Remember, it's not a game of brute force. More people make the mistake of gripping a dart too tightly than too loosely.
Try to use at least three of your fingers to hold the dart to give you more control. Chances are you'll discover through trial and error whether you do better with darts with longer or shorter barrels. Finding the barrel that's the right size for you is an important step in developing your game.
When aiming your dart, have your eye, the dart, and the target all in a line. This will help decrease errors caused by needless sideways actions of your arm. Your weight should favor your forward foot, though your back foot should hold enough weight to keep you balanced. It's not good to lean forward too much, because it throws your balance off. Once you get into the "groove" of playing darts, you'll find it's a really fun activity for when you hang out with your friends.
About the Author
If you are interested in learning to play darts knowing the rules for darts and being informed on various Darts technique will have you winning every game.
by admin on August 2nd, 2011 Tags: darts, darts probability, mathlessons, maths, nwrel, probability
Posted in Dart Board Cabinet | Comments Off
