This seems intuitive but would like a second opinion.
Powerball with 69 numbers. Need to choose 5 correct (order does not matter).
Prediction A: 60, 61, 64, 65, 68
Prediction B: 25, 35, 48, 59, 64
When I look at a list of 253 actual powerball drawings, the lowest number (slot 1) is never over 51. I know that 51 or higher for slot 1 is possible but is it correct to say that the likelihood of Prediction A is more of an edge case (due to a high number, 60 in this case, in slot 1)?
Thus, Prediction A is less likely to appear than Prediction B?
Slot 1 does not mean the first ball drawn. Rather, it is the lowest numbered ball after 5 balls are drawn.
Thanks.
It is not correct to say that prediction A is less likely than prediction B. There are many more possible draws with $25$ as the lowest number than with $60$ as lowest number, but any specific draw is $1$ chance in $69 \choose 5$. $1,2,3,4,5$ also has the same probability, but I would bet you have never seen it. The fallacy comes from intuitively lumping the cases into classes. $25,35,48,59,64$ doesn't have any features that stand out, so you might think of it as a normal draw. $60,61,64,65,68$ has all the numbers very high, so you think of that group, which is much smaller. That makes it much less likely to get a draw "like $60,61,64,65,68$" than a draw "like $25,35,48,59,64$"