National Lottery

Introduction

The first UK draw of the current National Lottery took place on Saturday 19th November 1994. Since then there have been over 1000 draws and the highest Jackpot available in that time was £42008610. However, this was shared amongst 3 winners. The highest Jackpot paid to a single winner is £22590829.

To play the National Lottery you need to be over 16 years old. You select 6 different numbers from 1 - 49. Each line of numbers you select costs £1. To win the Jackpot you need to match all 6 numbers from one of your lines to the first 6 numbers drawn from the lottery machine. There is also a 7th ball drawn known as the Bonus Ball. This ball is only used if you have matched 5 of the first 6 balls drawn, on one of your lines. If your 6th number then matches the bonus ball you win a substantial cash prize (though not as large as the Jackpot!). There are also cash prizes for matching 5, 4 or 3 numbers from your line to numbers drawn.

More information about the National Lottery plus details of every previous draw and many other statistics can be found at lottery.merseyworld.com.

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

 

Question 1
For the Jackpot, you need to match all 6 winning numbers.

(a)  How many ways are there of choosing six numbers from 49?
(b)  How many ways are there of ordering 6 numbers?
(c)  How many different lines of 6 numbers are there?

 

Question 2

(a)  What are the odds of winning the Jackpot if you buy just one line
of six numbers?		 1 in
(b)  How much would it cost to buy all the possible lines of numbers?    £

 

Question 3
For the second prize, you need to match exactly 5 out of the 6 winning numbers, plus the bonus number.

(a)  In how many different ways can you match 5 out of the 6 numbers?
(b)  How many ways are there of winning the second prize?
(c)  What are the odds of winning the second prize? 1 in

 

Question 4
You are guaranteed a £10 prize if you match exactly 3 out of the 6 winning numbers.

(a)  In how many ways can you select 3 numbers out of the 6 winning numbers?
(b)  For each of these selections, how many different lines could match that
selection of 3 numbers? (excluding tickets that would win higher prizes)
(c)  How many ways are there of winning £10?
(d)  What are the odds of winning £10? (To the nearest whole number) 1 in
(e)  If you buy one line of the same six numbers for both the Wednesday
and the Saturday draws, how many times should you expect to
win the £10 prize during one year? (To the nearest whole number)

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Produced by R.D.Geach June 2006
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