Transcript Odds Introduction - IGS KW Internet Service Provider/ISP

CAN YOU WIN ?
USING FRACTIONS TO CALCULATE ODDS
A coin is tossed.
What can happen ?
What is the chance
you will get a head ?
Heads
Tails
1
2
Two coins are tossed ?
How many possible results
What is the chance
you’d get 2 heads ?
1 1 1
  
4 2 2
1 tail, 1 head
2 tails
are there ?
2 heads
1 head, 1 tail
A die is tossed.
There are 6 possible results.
1
2
3
4
5
6
1
6
What is the chance you’d roll a 6 ?
36 6 6
Two dice are rolled.
How many different results are there ?
die 1
1
1
1
1
1
1
2
2
2
2
2
2
3
3
3
3
3
3
4
4
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
6
die 2
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
total
2
3
4
5
6
7
3
4
5
6
7
8
4
5
6
7
8
9
5
6
7
8
9 10
6
7
8
9 10 11
7
8
9 10 11 12
1
36
1
36
How many 7’s are there ?
1
36
6
1
36
What are your chances of rolling a 7 ?
1
36
6
36
1
36
or
1
6
A SIMPLE LOTTERY
There are 20 numbers, from 1 to 20, each on a different ball.
Two balls are to be selected at random.
You can win a prize if you correctly guess which numbers will be drawn.
What are the chances your first
selection will be correct ?
What are the chances your second
selection will be correct ?
What are the chances both your
selections will be correct ?
2
20
1
19
(assuming your first
choice was right)
1
2
1

20 19
10
=
1
190
( one chance in 190 )
Lotto 649
In Lotto 649 you can win the grand prize by correctly matching
the 6 numbers selected random from the numbers from 1 to 49 .
You have 6 chances out of 49 for your
1st
number to match
You have 5 chances out of 48 for your 2nd number to match
You have 4 chances out of 47 for your 3rd number to match
You have 3 chances out of 46 for your
4th
number to match
You have 2 chances out of 45 for your 5th number to match
You have 1 chance out of 44 for your 6th number to match
6
49
5
48
4
47
3
46
2
45
1
44
Lotto 649
To find the chance you’ll match all 6 numbers, the fractions
need to be multiplied together.
1
1
1
1
1
6
5
4
3
2
1





49 48 47 46 45 44
8
23
93
11
To what simplified fraction does this reduce ?
1
49  8  47  23  3  11
=
1
13 983 816
You have about 1 chance in 14 million to win 1st prize !!!
GOOD LUCK !
Super 7
Here you must match 7 numbers out of 47 (747) to
win the first prize.
What set of fractions must you multiply together to
calculate the odds of winning the first prize ?
1
1
1
1
1
1
7
6
5
4
3
2
1






47 46 45 44 43 42 41
23
9
3
This reduces to
11
1
62 891 499
6
1
(one chance in about 63 million)
However, on each ticket you get 3 sets of numbers, so your odds
of winning the first prize are about 1 in 21 million.
Lottario
In Lottario you must match 6 numbers out of 45.
Each ticket gives you 2 sets of possible winning numbers.
What are the chances you’ll win the first prize ?
1
1
1
1
1
6
5
4
3 2
1



 
45 44 43 42 41 40
93
7
11
This reduces to
20
1
8 145 060
So the odds that you could win first prize are about 1 in 4 million .
Lottery Worksheet
Lotto 649
Super 7
Lottario
6
5
4
3
2
1





49 48 47 46 45 44

7
6
5
4
3
2
1






47 46 45 44 43 42 41

6
5
4
3 2
1



 
45 44 43 42 41 40
