Download Odds of Winning Jackpot Triple Play: Matching Number Combinations Probabilities and more Study notes Probability and Statistics in PDF only on Docsity!
How to Calculate the Probabilities of Winning
the Four JACKPOT TRIPLE PLAY Prize Levels:
JACKPOT TRIPLE PLAY ™^ numbers are drawn from a set of 46 numbers. Since the order
of the items chosen is irrelevant, the applicable probability rule is the formula to determine
combinations.
Before calculating the odds for the different prize levels, calculate the total number of
combinations possible.
Calculate how many combinations of 6 numbers can be drawn from 46 unique
numbers:
The formula is as follows:
where! indicates a factorial, i. e. , n! = n ∗ (n − 1) ∗ (n − 2) ∗.. .∗ 2 ∗ 1
Thus, there are 9,366,819 different ways in which 6 numbers can be chosen from a
total of 46 unique numbers.
Since a Jackpot Triple Play ticket consists of three possible sets of winning numbers, the
next step in calculating the odds is to determine the probability of winning on a single set:
Match all six numbers in a single set (1 in 9,366,819 odds)
Calculate the number of ways in which 6 numbers can be chosen correctly out of 6
numbers drawn from 46 unique numbers.
The formula is as follows:
�(46 − 6)^ − (6 − 6)�! (6 − 6)!
(note: 0!=1)
This means that there is only 1 way in which 6 numbers out of 6 numbers drawn
from a field of 46 numbers can be chosen correctly.
Thus, there is only 1 chance in 9,366,819 of correctly choosing all six numbers
drawn in JACKPOT TRIPLE PLAY in a single set of numbers.
Match five numbers in a single set (1 in 39,028.41 odds)
Calculate the number of ways in which 5 numbers can be chosen correctly out of 6
numbers drawn from 46 unique numbers.
The formula is as follows:
This means that there are 240 different ways in which 5 numbers out of 6 numbers
drawn from a field of 46 numbers can be chosen correctly.
Thus, the chances are 240 in 9,366,819 of correctly choosing 5 out of 6 numbers
drawn in JACKPOT TRIPLE PLAY in a single set of numbers, which can be
reduced to 1 chance in 39,028.41.
Match four numbers in a single set (1 in 800.58 odds)
Calculate the number of ways in which 4 numbers can be chosen correctly out of 6
numbers drawn from 46 unique numbers.
The formula is as follows:
4! (6 − 4)! ∗^
4! 2! ∗^
2 ∗^
38! 2 = 15^ ∗^
This means that there are 11,700 different ways in which 4 numbers out of 6
numbers drawn from a field of 46 numbers can be chosen correctly.
Thus, the chances are 11,700 in 9,366,819 of correctly choosing 4 out of 6 numbers
drawn in JACKPOT TRIPLE PLAY in a single set of numbers, which can be
reduced to 1 chance in 800.58.
Match three numbers in a single set (1 in 47.40 odds)
Calculate the number of ways in which 3 numbers can be chosen correctly out of 6
numbers drawn from 46 unique numbers.
The formula is as follows:
3! (6 − 3)! ∗^
3! 3! ∗^
3 ∗ 2 ∗^
37! 3 ∗ 2 = 20^ ∗^
This means that there are 197,600 different ways in which 3 numbers out of 6
numbers drawn from a field of 46 numbers can be chosen correctly.
Thus, the chances are 197,600 in 9,366,819 of correctly choosing 3 out of 6
numbers drawn in JACKPOT TRIPLE PLAY in a single set of numbers, which can
be reduced to 1 chance in 47.40.
Match four of six numbers at least once on a single ticket (1 in 267.19 odds)
Since the chances of a single set matching four of six numbers are 11,700 in
9,366,819, the chances of a single set not matching four of six numbers are
9,355,119 in 9,366,819. The chances of all three sets not matching four of six
numbers are
9,366,819 ∗^
9,366,819 ∗^
Conversely, the chances of at least one set matching four of six numbers are
821,819,391,589,483,931,259 =^
Thus, the chances are 3,075,734,096,128,781,100 in 821,819,391,589,483,931,
of correctly choosing 4 out of 6 numbers drawn in JACKPOT TRIPLE PLAY at least
once on a single ticket, which can be reduced to 1 chance in 267.19.
Match three of six numbers at least once on a single ticket (1 in 16.14 odds)
Since the chances of a single set matching three of six numbers are 197,600 in
9,366,819, the chances of a single set not matching three of six numbers are
9,169,219 in 9,366,819. The chances of all three sets not matching three of six
numbers are
Conversely, the chances of at least one set matching three of six numbers are
Thus, the chances are 50,921,182,102,633,200,800 in
821,819,391,589,483,931,259 of correctly choosing 3 out of 6 numbers drawn in
JACKPOT TRIPLE PLAY at least once on a single ticket, which can be reduced to 1
chance in 16.14.
Match 3, 4, 5, or 6 numbers at least once on a single ticket (1 in 15.24 odds)
To calculate the number of ways in which 3, 4, 5, or 6 numbers can be chosen
correctly at least once out of 6 numbers drawn from 46 unique numbers, the
chances of each possibility are added together. From the steps above, we have:
821,819,391,589,483,931,259 +^
821,819,391,589,483,931,259 +^
Thus, the chances are 54,060,348,646,744,500,000 in
821,819,391,589,483,931,259 of correctly choosing 3, 4, 5, or 6 out of 6 numbers in
JACKPOT TRIPLE PLAY at least once on a single ticket, which can be reduced to 1
chance in 15.24.
How to Calculate the Probabilities of Winning
the Combo JACKPOT TRIPLE PLAY Prize Levels:
To calculate the odds on the Combo play prizes, we need to know how each situation can
occur. The chances for each possibility occurring are calculated and added together to get
the total chances for that number of matches occurring on a ticket.
From the steps in the base game above, we know the chances of getting 3, 4, 5, or 6
matches in a single set. For purposes of the Combo play, the chances of getting 0, 1, or 2
matches in a single set are also calculated, using the same formula as above. To recap,
we get the following:
Match 6 – 1 in 9,366,
Match 5 – 240 in 9,366,
Match 4 – 11,700 in 9,366,
Match 3 – 197,600 in 9,366,
Match 2 – 1,370,850 in 9,366,
Match 1 – 3,948,048 in 9,366,
Match 0 – 3,838,380 in 9,366,
As an example of how the calculations are derived, the steps for calculating the chances of
matching 4 numbers in the Combo play will be done.
Four occurrences of matching numbers on a single ticket can occur in several ways:
4 matches in set 1, no matches in set 2, and no matches in set 3 (4,0,0)
No matches in set 1, 4 matches in set 2, and no matches in set 3 (0,4,0)
No matches in set 1, no matches in set 2, and 4 matches in set 3 (0,0,4)
3 matches in set 1, 1 match in set 2, and no matches in set 3 (3,1,0)
3 matches in set 1, no matches in set 2, and 1 match in set 3 (3,0,1)
1 match in set 1, 3 matches in set 2, and no matches in set 3 (1,3,0)
1 match in set 1, no match in set 2, and 3 matches in set 3 (1,0,3)
No matches in set 1, 3 matches in set 2, and 1 match in set 3 (0,3,1)
No matches in set 1, 1 match in set 2, and 3 matches in set 3 (0,1,3)
2 matches in set 1, 2 matches in set 2, and no matches in set 3 (2,2,0)
2 matches in set 1, no matches in set 2, and 2 matches in set 3 (2,0,2)
No matches in set 1, 2 matches in set 2, and 2 matches in set 3 (0,2,2)
2 matches in set 1, 1 match in set 2, and 1 match in set 3 (2,1,1)
1 match in set 1, 2 matches in set 2, and 1 match in set 3 (1,2,1)
1 match in set 1, 1 match in set 2, and 2 matches in set 3 (1,1,2)
The odds for each of these situations is calculated, then they are all added together to
determine the chances of matching 4 numbers on a ticket. (Note that they have been
This same procedure can be followed to determine the chances of matching each of the
possible prize levels on a JACKPOT TRIPLE PLAY Combo play. For the top prize of
matching 10 or more, the chances for matching each possible number from 10 to 18 are
calculated and then summed together to get the chances for matching 10 or more.
