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Topic: What probability a six-number lottery ticket has 3 consecutive
numbers, the others not?

Replies: 7   Last Post: Feb 12, 2009 11:18 PM

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rossum

Posts: 731
Registered: 12/13/04
Re: What probability a six-number lottery ticket has 3 consecutive numbers, the others not?
Posted: Feb 11, 2009 6:39 AM
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On Wed, 11 Feb 2009 00:52:11 -0800 (PST), Archie
<kohmover123@yahoo.com> wrote:

>Say you can choose six numbers out of 59. What is the probability that
>three (and only three) will be consecutive? This is complicated by the
>fact that numbers appear in order from least to greatest. What if the
>six numbers contain 2 sets of 3 consecutive numbers?
>
>I'm not finding any easy formula for this.
>
>Thanks!

Do you pick six numbers at random and use the order they are picked
in, or do you pick six numbers and then sort them before looking for
runs of three? The probabilities are different.

For three consecutive numbers, then they must fall into one of the
following patterns:

abcxxx
xabcxx
xxabcx
xxxabc

where abc are three consecutive ascending numbers and the x's are any
other numbers. Work out the probabilities for each pattern and sum
them.

Two sets of three has the pattern: abcefg.

rossum




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