I'm trying to plot a probability function that has large fractions between 0 and 1, but Plot returns an empty graph.

The strange thing is that when I adjust the sampling using the output slider or adjust the line thickness, I can briefly see the graph before it goes away once I let go.

I'm currently on version 11.0.

Here's my code:

func[x_] := 365!/((365 - x)! 365^x)
Plot[func[x], {x, 0, 100}]

I've also tried defining func[x_] as N[...] (calculating the numerical value), but that makes no difference.

  • $\begingroup$ I don't know how to fix this, but if all you care about is how the function looks like you can get around the problem by explicitly evaluating it for a list of values: ListLinePlot[Table[{x, func[x]}, {x, 100}]] $\endgroup$
    – yohbs
    Apr 27 '17 at 2:50
  • $\begingroup$ @yohbs That's okay for now, but I noticed this problem with several other functions involving really large or tiny numbers (can't recall them right now). I'm wondering if this is a bug or not. $\endgroup$
    – jLee
    Apr 27 '17 at 3:33
  • $\begingroup$ @jLee I get a plot using your code on MMA 11.1.0 . $\endgroup$ Apr 27 '17 at 4:11
  • $\begingroup$ @jLee I get a plot using $Version "11.1.0 for Mac OS X x86 (64-bit) (March 16, 2017)" $\endgroup$
    – evanb
    Apr 27 '17 at 6:03

For functions that might not work directly even on 64-bit machines, you might consider the old-fashioned way using logs:

func[x_] := Exp[LogGamma[365 + 1] - LogGamma[365 - x + 1] - x Log[365]]
Plot[func[x], {x, 0, 100}]

Function plot


Use FactorialPower[] instead to sidestep any possible overflow issues:

Plot[FactorialPower[365, x] 365^-x, {x, 0, 100}]

function plot



I am facing the same issue of seeing an empty plot.

"11.0.1 for Microsoft Windows (32-bit)"

Another alternative is to use DiscretePlot,

func[x_] := 365!/((365 - x)!* 365^x);

DiscretePlot[func[x], {x, 0, 100}, Filling -> None, Joined -> True]


  • 1
    $\begingroup$ Perhaps your issue is that you are on a 32-bit OS. On a Mac OS X x86 (64-bit) I have no problem. $\endgroup$
    – Bob Hanlon
    Apr 27 '17 at 6:01
  • $\begingroup$ @BobHanlon Maybe that is the case. $\endgroup$
    – zhk
    Apr 27 '17 at 6:05
  • $\begingroup$ @BobHanlon that may be the case since I ran it on my 64 bit Mac OS X machine and it worked, but not my 32 bit Windows machine $\endgroup$
    – jLee
    May 2 '17 at 15:59

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