# Math Help - Basic question on chance

1. ## Basic question on chance

I left school in the '60s, and I've forgotten most of the statistics I ever knew, so I expect this question is easily answered.

You have one of those spinning discs that has a red, a green and a blue sector (thus producing white). If you throw a dart at it, you have a 1 in 3 chance of hitting red, so over a large number of throws, say 9000, you can expect to score 3000 hits on red. But suppose you divide them into 1000 groups of 9 consecutive throws, and score each session - 3/9, 2/9, 5/9, etc. Two questions:

1. If 3/9 is your average score, does that mean it is also your most common score?

2. Will 2/9 and 4/9 occur with equal frequency?

2. Originally Posted by Terpsichore
I left school in the '60s, and I've forgotten most of the statistics I ever knew, so I expect this question is easily answered.

You have one of those spinning discs that has a red, a green and a blue sector (thus producing white). If you throw a dart at it, you have a 1 in 3 chance of hitting red, so over a large number of throws, say 9000, you can expect to score 3000 hits on red. But suppose you divide them into 1000 groups of 9 consecutive throws, and score each session - 3/9, 2/9, 5/9, etc. Two questions:

1. If 3/9 is your average score, does that mean it is also your most common score?

2. Will 2/9 and 4/9 occur with equal frequency?
The the number X of reds in nine throws is binomially distributed like so:

$\mathrm{P}(X=k)=\binom{9}{k}\cdot \left(\frac{1}{3}\right)^k\cdot \left(1-\frac{1}{3}\right)^{9-k}$