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How to work out binomial distribution?
I really do not undersand normal distribution and I need it for my Stats. I've got this question and if anyone could talk it through for me that would be great thanks!
Megan throws darts at a target. She can hit the target 7 times in 9 throws. She throws 3 darts.
Assuming a binomial 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
Thankyou!
Hi,
She can hit the target 3,2,1, or 0 times. There are 2³ or 8 possible outcomes, which divide up into the binomial expansion coefficients for each result.
3 hits can occur only one way.
2 hits can occur 3 ways, YYN, YNY, or NYY.
1 hit can occur 3 ways, YNN, NYN, or NNY.
0 hits occur one way, NNN
When the odds of her success on a throw is 7/9 then the odds of missing is 2/9. The results could be:
3nCr3(7/9)^3(2/9)^0 = .011 = 1.1% probability of 3 hits
3nCr2(7/9)^2(2/9)^1 = .115 = 11.5% probability of 2 hits
3nCr1(7/9)^1(2/9)^2 = .403 = 40.3% probability of 1 hit
3nCr0(7/9)^0(2/9)^3 = .471 = 47.1% probability of 0 hits
3nCr3 = 1
3nCr2 = 3
3nCr1 = 3
3nCr0 = 1
These are the binomial coefficients above. They are multiplied times the 7/9 likelihood raised to the number of hits times the 2/9 likelihood of missing the target raised to the number of misses.
3nCr2(7/9)^2(2/9)^1 = .115 = 11.5% probability of 2 hits
There is an 11.5% probability of 2 exactly hits.
I hope that helps!! 
Becoming A Master Of Darts Dart
Developing skill and accuracy can be done in a number of ways, but hitting a bulls eye is probably one of the more challenging arts to master. Darts dart, a game where you throw darts at a target on your wall, epitomizes this challenge and can be a sport from the most social to the most professional.
You can start off simply, with a dart board and a couple of darts. The "clock" board, a circular board is made up of different segments and has numbers running around the perimeter of the circle. Each segment and number contributes to different points, depending on where your dart lands. The bulls eye is the red circle in the middle of the board, however it is often known as the double bulls eye. The green ring on the outside of the red circle is the outer bulls eye. Dart darts can be played with children or friends and makes a good game at social gatherings.
And then you can start taking it more seriously as a sport, acquiring better darts and testing your skill. For darts dart, you can really get professional. You can get wooden darts, brass darts, silver or nickel darts and tungsten darts – in other words, all made up of different metals. There are also different types of shafts for darts, namely plastic, composite, solid aluminum or spinning. There are also different types of flights, which refers to the wings on the darts. You can get hard flights (made of polyester plastic), nylon flights (made of nylon fabric) or soft flights (made of plastic sheet). You can also get a soft-tip dart or a steel-tip dart. Boards can vary too and you can even get a board in a wooden box, which opens up with a chalk board on the inside of the wooden doors, making it easy to keep score.
Professional darts dart games take place globally where there is an official Professional Darts Corporation in the United Kingdom and a World Darts Federation . They host dart championships all over the world. A game from back in medieval England, the rules of darts dart vary, but basically you need to stand behind a drawn line and throw from a distance equal for everyone partaking. Traditionally, this distance is 7 ft. 9 ¼ inches from the board. In most games, each person is allowed three throws. Often darts can fall off a board when thrown and in most instances, these throws are discounted.
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