Odds and Probabilities

 

What are the odds?...
Some of these Stats are directly related to Australian only.

Winning Powerball (Australian lotto draw) 27,489,577
Winning Oz Lotto (Australian lotto draw) 8,145,060
Winning Tattslotto (Australian lotto draw) 2,036,265
Killed by lightning 1,603,250
Winning Six from 38 pools 1,380,340
Dying from venomous bite/sting 1,159,364
Being murdered (female) 79,365
Being blackmailed 52,632
Being murdered (male) 45,249
Being Kidnapped 33,223
Having malaria 21,739
Being in prison (female) 6757
Trifecta (13-horse race) 1716
Being in prison (male) 396
Having car stolen 142
Roulette number coming up 37
Five successive tosses in two-up 32
Pulling an ace out of a deck of cards 13
Rolling a 7 or 11 in craps 4.5
Dying from heart disease 4.0
Scratch Tickets 3.0 - 6.0
Household with couple and no children 3.0
Australian living in Melbourne or Sydney 2.6
Marriage ending in divorce 2.3
Married couple aged within two years of each other 2.2
Bride being older than 26 at first wedding 2.0
Source: Herald Sun 11/5/99:
Maquarie University; ABS; Australian Severe Weather Kattron Lightning Strike Data Page

 

Some other interesting odds for you:

  • Being struck by lightning -- 1 in 10,456 (lifetime) 
  • Being Murdered -- 1 in 140 (lifetime) 
  • Having your car Stolen -- 1 in 159 (annual risk) 
  • Getting married -- 3 in 4 (life time risk) 
  • Seriously injuring yourself while shaving -- 1 in 5,844 (annual risk) 
  • Dying in an auto accident -- 1 in 75 (lifetime risk) 
  • Going to prison this year -- 1 in 139 
  • Getting breast implants -- 1 in 65 
  • Dying from heart disease -- 1 in 6 (lifetime risk) 
  • Going to Disney world this year -- 1 in 9 
  • Eating at McDonalds today -- 1 in 12 
  • Getting fat -- 1 in 4 (lifetime risk) 
  • Being injured by your toilet bowl cleaner -- 1 in 173,972 (annual risk) 
  • Hiring a sleazy lawyer -- 1 in 8 
  • Dying from falling out out of your bed or chair -- 1 in 513,142 
  • Developing a mental disorder this year -- 1 in 4 
  • Being stuck and killed by a falling aircraft -- 1 in 25 million 
  • Getting food poisoning -- 1 in 8 (annual risk) 
  • Freezing to death -- 1 in 780,938 (annual risk) 
  • Committing suicide -- 1 in 71 (lifetime risk) 
  • Dying in a sporting accident this year: 
  • Mountain climbing -- 1 in 167 (1 in 5 lifetime)
  • Hang Gliding -- 1 in 4,444
  • Skydiving -- 1 in 86,000 jumps
  • Auto Racing -- 1 in 1000 to 1 in 5000 depending on type
  • Motorcycling -- 1 in 1000 
  • Running -- 1 in 10,000 
  • Boating and Swimming -- 1 in 36,000 
  • Playing football -- 1 in 57,000 
  • Bicycling -- 1 in 130,000 
  • Safest Sports -- Badminton and Ping Pong

What you need for a typical win in a lottery
(excluding supplementary numbers variations)
Correct balls General prize won Odds
6 $2,000,000 1 in 13,983,816
5 $5,000 1 in 54201
4 $80 1 in 1032
3 $0 1 in 57
2 $0 1 in 8
1 $0 1 in 2
0 $0 1 in 2
Here's a little Lotto Draw.
Pick 6 numbers and see how many turn up!
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49
Your selection:
Lottery result:

Probabilities

If you attempt to guess one number chosen from 49 lottery balls then the probability that you are correct is 1/49. If you have a second attempt, and the previous ball is not replaced, then the probability is 1/48.

If you choose six numbers then the probability that one of them is the same as the first ball drawn is 6/49. Given that the first number is chosen correctly then the probability for drawing the second number correctly is 5/48. The probability of choosing all six numbers correctly is:

6 / 49 x 5 / 48 x 4 / 47 x 3 / 46 x 2 / 45 x 1 / 44 = 1 / 13,983,816

So, for example, if you have one attempt per week then you could expect to win, on average, once during the next 268,920 years!

Calculating The Odds explained from www.howstuffworks.com
Let's take a look at how to calculate the odds of picking the right number for a typical Lotto game. In order to win our example game, you have to pick the correct six numbers from 50 possible balls. The order in which the numbers are picked is not important; you just have to pick the correct six numbers.

The odds of picking a single correct number depend on how many balls have been chosen already. For instance, let's say none of the six numbers had been picked yet and you had to guess just one number correctly. Since there are 50 numbers to chose from, and since six balls are going to be picked, you have six tries at picking the number correctly. The odds of picking one number correctly are 50/6 = 8.33:1.

Using a similar calculation, we can determine the odds of picking another number correctly after one number has already been drawn. We know there are 49 balls left, and that five more balls will be drawn. So the odds of picking a number correctly after one has been drawn are 49/5 = 9.8:1.

Now let's say five numbers have been picked and you have to guess what the last number is going to be. There are only 45 balls left to choose from, but you only get one shot at it, so your odds are only 45:1.

In a similar manner, we can calculate the odds of picking the right number when two, three, four and five balls have been drawn. You know the odds of a coin toss resulting in heads are 1/2 = 2:1. The odds of two consecutive tosses both resulting in heads are 1/2 x 1/2 = 4:1. The odds of three consecutive tosses all resulting in heads are 1/2 x 1/2 x 1/2 = 8:1. The odds of picking all six lottery numbers are calculated the same way -- by multiplying together the odds of each individual event. In this case:

50/6 x 49/5 x 48/4 x 47/3 x 46/2 x 45/1 = 15,890,700:1

Some states have been increasing or decreasing the number of balls in order to change the odds. If the odds are too easy, then someone will win the jackpot almost every week and the prize will never grow. Large jackpots tend to drive more ticket sales. If the prize is not large enough, ticket sales can decrease. On the other hand, if the odds against winning are too great, ticket sales can also decline. It is important for each lottery to find the right balance between the odds and the number of people playing.

If you add just one number to our hypothetical lottery, so people now have to pick from 51 balls, the odds increase to 18,009,460:1.

Powerball
Some states have joined together to run multi-state Powerball lotteries. Since so many people can play, they need a game with really large odds against winning. In this multi-state Powerball lottery game, the winner has to pick the correct five numbers from a set of 50 balls, and they have to pick the single correct number from a separate set of 36 balls. So the odds of picking the correct number in this game are:

36 x (50/5 x 49/4 x 48/3 x 47/2 x 46/1) = 76,275,360:1

So let's say you pick the right six numbers and win a $10 million jackpot -- you're going to get $10 million, right? Well, sort of…

 

Home