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Lottery - odds of getting no numbers at all
5 Answers
What are the odds on my lottery ticket not matching a single lottery number? i.e the opposite to having all 6 numbers matching..? It seems to happen fairly often..!
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Here's a bit of maths for you.
'Hit' means that the number which pops out of the machine is one which you've selected. 'Miss' means that the machine produces a number which is not in your selection.
When the first number is drawn, there are 49 balls in the machine. 6 of these will produce a Hit and 43 will produce a Miss. So, the probability of getting a Miss is 43/49.
Assuming this happens, there are then 48 balls in the machine. 6 of these will provide a Hit and 42 will give a MIss. So the probability of the second ball being a Miss is is 42/48.
Assuming that we've now had two Misses, the probability of the 3rd ball also being a Miss is now 41/47.
If we keep getting Misses, the probabilities of the last 3 balls each being a Miss are 40/46, 39/45 and 38/44.
To calculate the probability of all 6 balls being a Miss, we simply need to multiply those six probabilities together. Rounding off to 3 significant figures, this shows that the probability of getting 6 Misses (i.e. no numbers at all on your ticket) is 43.6%. Conversely, the probability of getting at least one number is 56.4%. This means that just under half of your selections should be 'total blanks' with just over a half having at least one number present.
Chris
'Hit' means that the number which pops out of the machine is one which you've selected. 'Miss' means that the machine produces a number which is not in your selection.
When the first number is drawn, there are 49 balls in the machine. 6 of these will produce a Hit and 43 will produce a Miss. So, the probability of getting a Miss is 43/49.
Assuming this happens, there are then 48 balls in the machine. 6 of these will provide a Hit and 42 will give a MIss. So the probability of the second ball being a Miss is is 42/48.
Assuming that we've now had two Misses, the probability of the 3rd ball also being a Miss is now 41/47.
If we keep getting Misses, the probabilities of the last 3 balls each being a Miss are 40/46, 39/45 and 38/44.
To calculate the probability of all 6 balls being a Miss, we simply need to multiply those six probabilities together. Rounding off to 3 significant figures, this shows that the probability of getting 6 Misses (i.e. no numbers at all on your ticket) is 43.6%. Conversely, the probability of getting at least one number is 56.4%. This means that just under half of your selections should be 'total blanks' with just over a half having at least one number present.
Chris
I`ve also always had a free ticket with a "no win" daily play but my usual shop has closed and none of the other shops in Chippenham will issue one, Woolworths, Sainsburys and Somerfield say they don`t do it. It states on the National Lottery web site that zero is a free ticket so where do I go from here?
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