1. Probability distributions
Statistics 1

2. UK National lottery
Six balls and one bonus ball are drawn without replacement from a set of individually numbered balls with numbers in the range 1 – 49

3. Frequency table
If you were to play the lottery, which six numbers would you choose?
Source: [9 Aug 2011]

4. Prize money The entry fee to the Lotto draw is £1 per board.
Matching numbers
Prize
3 numbers
£10
4 numbers
22% of the remaining fund
5 numbers
10% of the remaining fund
5 numbers and bonus ball
16% of the remaining fund
6 numbers
52% of the remaining fund
Source: [6 Aug 2011]

5. Odds
What’s the probability of drawing 6 numbers from a set of 49 numbers?

6. More odds What’s the probability of not winning anything?
Matching numbers
Prize
Odds of winning
3 numbers
£10
1/57
4 numbers
£48
1/1033
5 numbers
£1,025
1/55492
5 numbers and bonus ball
£66,277 1/
6 numbers
£3,877,209 1/
Source: [6 Aug 2011]

7. Probability distribution
Construct a probability distribution for the above table
Matching numbers
Estimated win
Odds of winning
3 numbers
£10
1/57
4 numbers
£62
1/1033
5 numbers
£1,500
1/55492
5 numbers and bonus ball
£100,000 1/
6 numbers
£2,000,000 1/
Source: [6 Aug 2011]

8. Expected value
Calculate the expected value and the standard deviation for the above distribution

9. Useful links Lottery odds