"Combination" means the group of numbers selected, irrespective of the order in which they are drawn.

For example, the information content of any event easy to calculate, by the formula I ( E ) : log Pr ( E ) log ( P ).

Another example of such a game is Mega Millions, albeit with different jackpot odds.

Why is there no Bonus Ball on my ticket?Find out more about the role of the Bonus Ball below.H ( X ) x p X ( x ) log p X ( x ) x p X ( x ) I X ( x ) d e f E I X ( x ) displaystyle beginalignedat2mathrm H (X) sum _x-p_Xleft(xright)log p_Xleft(xright).( n k )!This means that there are 6 - n losing numbers, which are chosen from the 43 losing numbers in ( 43 6 n ) displaystyle 43 choose 6-n ways.The longer odds in the 'Match 5 Bonus' tier mean that far fewer players are likely to win in this category.Displaystyle beginalignedoperatorname I _X(textlose) -log _2p_X(textlose)-log _2!tfrac.0317times 10-7text shannons.Endaligned References edit External links edit.Irish Lotto Bonus Ball Betting Some bookmakers offer bets on one or more of the Bonus Balls from Irish Lotto, Lotto Plus 1 and Lotto Plus.For example, winning in the example Choosing 6 from 49 above is a Bernoulli-distributed random variable X displaystyle X with a 1/13,983,816 chance of winning success We write X B e r n o u l l i ( p ) B ( 1,.Staking 1 at these odds returns 75,000 plus your initial 1 stake.The generalisation of this formula is called the hypergeometric distribution.An alternative method of calculating the odds is to note that the probability of the first ball corresponding to one of the six chosen is 6/49; the probability of the second ball corresponding to one of the remaining five chosen is 5/48; and.EuroMillions works differently in that the additional numbers in that game, the Lucky Stars, are taken from a separate pool and must be matched along with the main numbers to claim the jackpot.

This makes it easy to calculate quantities of interest from information theory.

The general formula for B displaystyle B matching balls in a N displaystyle N choose K displaystyle K lottery with one bonus ball from the N displaystyle N pool of balls is: K B N K ( K B ) ( N K.How does it work?As described in the " other scores " section above, the number of ways one can obtain a score of 5 from a single ticket is ( 6 5 ) ( 43 1 ) 258 textstyle 6 choose.3 Information theoretic results edit Further information: Quantities of information As a discrete probability space, the probability of any particular lottery outcome is atomic, meaning it greater than zero.Lotto, bonus Ball, to play Lotto, you are required to select six numbers from 1.Lotto Odds page to find out more about the chances of winning in all the different prize tiers.This continues until the sixth number has been drawn, giving the final calculation, which can also be written as 49!

Odds Of Winning, prize, match 5 Bonus 1 in 7,509,579 1 million, match 5 1 in 144,415 1,750.