Wikipedia:Reference desk/Archives/Mathematics/2016 January 9

= January 9 =

Lotto odds
I'm using the hypergeometric distribution function (as shown on the lottery mathematics article) to work out the odds of the UK Lotto

Calculating the odds of getting 0-6 numbers is easy because it only differs slightly from the table in the article (59 versus 49 balls). However, the U.K. Lotto differs from the example because as well as drawing six balls, they also draw a bonus ball. This is then taken into account if you get five numbers. So how do I calculate the odds of getting 5 numbers plus the bonus ball? (I know the answer is shown on the National Lottery article - I'm interested in how it's worked out).2.120.39.235 (talk) 20:01, 9 January 2016 (UTC)


 * So U.K. Lotto draws six balls from 59 balls and then draw one ball from (59 - 6) balls. And then you win if you get 5 numbers correct out of 7 numbers. Am I correct? 175.45.116.66 (talk) 23:38, 10 January 2016 (UTC)
 * Not quite - you win if you get the 6 standard numbers. If you get 5 of the standard numbers plus the bonus ball, you get a lesser prize (though it's still a significant chunk of cash).
 * To answer the question - consider the case where a player matches any 6 balls out of the 7 drawn - this is the combination of "5 plus bonus ball" and "6 without bonus ball". So the chance of "5 plus bonus" is the chance of matching 6 of the 7 balls, minus the chance of matching the 6 standard balls. P(5 plus bonus) = P(6 of 7) - P(Jackpot). MChesterMC (talk) 10:24, 11 January 2016 (UTC)

Characteristics of the Toroidal Cross-sections.
For a Torus symmetric around the Z-axis, the cross sections at constant Z are rather easy to describe (circle, expanding to an area between two concentric circles and then back to a circle.) Is there *anything* useful/interesting/easily described for the cross sections at constant X (or Y). It goes sort of (point, something looks like an ellipse to a pinched waist to two things that eventually turn into circles and then back. The equation (x^2+y^2+z^2 + R^2 - r^2)^2 = 4R^2(x^2+y^2) doesn't appear to help much. (are they easier to describe with Polar co-ordinates????)Naraht (talk) 22:07, 9 January 2016 (UTC)


 * For a fixed value of x the equation (x2+y2+z2+R2−r2)2−4R2(x2+y2) = 0 provides an equation in y and z that describes the curves you are looking for. Point for x2=(R+r)2. Something like an ellipse for (R−r)2<x2<(R+r)2. A pinched waist for x2=(R−r)2. Two things for 0<x2<(R−r)2. Circles for x=0. Bo Jacoby (talk) 22:45, 9 January 2016 (UTC).
 * I understand that, but my question is more, what shapes are they? For example, when x is exactly x2=(R−r)2, it has a pinched waist down to zero, but is there a name for that shape?Naraht (talk) 01:12, 10 January 2016 (UTC)
 * See Spiric section. More generally Toric section for any slice of a torus. See also Hippopede. --RDBury (talk) 04:13, 10 January 2016 (UTC)
 * Thank you very much...Naraht (talk) 14:44, 12 January 2016 (UTC)