Multiple lawsujts allege that area gambling establishments, on multiple occasions, doctored equipment so as to give Birmingham mayor Larry Langford tens of thousands of dollars in winnjngs.

Langford, already in prison for scores of corruption-related charges, has not denied winning the money; he does deny that the machines were doctored.

We do not know exactly what the probability of winning the jackpot on a mad1ine that has 11ot been doctored might be, but we can make some intelligent guesses. Suppose thilt Langford on three occm,ions bet $1 ,rnd won $25,000. For c,,ch jackpot, in order to bre,1k even, ,1 gambling L'Stablishmcnt needs 24,999 people who bet $1

,rnd do not win. So we might infer that the probability of winning when betting a dollar 1s ... omcwhere in the neighborhood of 1/ 25, 000. If the e!>tablishment wants to make,, profit, which it docs, the probability would have to be even lower, but let us ignore this foct.

What 1s the prob,1bility that Lrngford would win the jad.pot three tim~ in a row when playing three times on undoctored machit11. '.S ?