Question Number 186901 by Beginner last updated on 11/Feb/23
Answered by Frix last updated on 12/Feb/23
![The chance for the jackpot is P=(1/C_7 ^(40) )=(1/(18 643 560)) The chance to not win in n games is (1−P)^n =(((18 643 559)/(18 643 560)))^n The chance to win at least once is 1−(1−P)^n n=15×30×52=23400 ⇒ answer is ≈.00125 or .125% [For a 50% chance you must play at least 12 922 732 times]](https://www.tinkutara.com/question/Q186915.png)
$$\mathrm{The}\:\mathrm{chance}\:\mathrm{for}\:\mathrm{the}\:\mathrm{jackpot}\:\mathrm{is} \\ $$$${P}=\frac{\mathrm{1}}{{C}_{\mathrm{7}} ^{\mathrm{40}} }=\frac{\mathrm{1}}{\mathrm{18}\:\mathrm{643}\:\mathrm{560}} \\ $$$$\mathrm{The}\:\mathrm{chance}\:\mathrm{to}\:{not}\:\mathrm{win}\:\mathrm{in}\:{n}\:\mathrm{games}\:\mathrm{is} \\ $$$$\left(\mathrm{1}−{P}\right)^{{n}} =\left(\frac{\mathrm{18}\:\mathrm{643}\:\mathrm{559}}{\mathrm{18}\:\mathrm{643}\:\mathrm{560}}\right)^{{n}} \\ $$$$\mathrm{The}\:\mathrm{chance}\:\mathrm{to}\:\mathrm{win}\:\mathrm{at}\:\mathrm{least}\:\mathrm{once}\:\mathrm{is} \\ $$$$\mathrm{1}−\left(\mathrm{1}−{P}\right)^{{n}} \\ $$$${n}=\mathrm{15}×\mathrm{30}×\mathrm{52}=\mathrm{23400} \\ $$$$\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\approx.\mathrm{00125}\:\mathrm{or}\:.\mathrm{125\%} \\ $$$$ \\ $$$$\left[\mathrm{For}\:\mathrm{a}\:\mathrm{50\%}\:\mathrm{chance}\:\mathrm{you}\:\mathrm{must}\:\mathrm{play}\:\mathrm{at}\:\mathrm{least}\right. \\ $$$$\left.\mathrm{12}\:\mathrm{922}\:\mathrm{732}\:\mathrm{times}\right] \\ $$
Commented by Beginner last updated on 12/Feb/23
$${Thanks} \\ $$