i have 5 tickets for a lottery that contains a total of 100.000 tickets. 100 tickets are drawn, what are the chances of me winning?

Guest Sep 16, 2014

#2**+8 **

i have 5 tickets for a lottery that contains a total of 100.000 tickets. 100 tickets are drawn, what are the chances of me winning?

Im splitting them into 100 winning and 99900 losing tickets

1-P(5lose)

1-(99900C5/100000C5)

Very close to 5/1000 = 1/200

That's what I think anyway.

Melody
Sep 16, 2014

#1**+5 **

I asume the total number of tickets is 10^{5}

The chance that *none* of your 5 is drawn is approximately (1-5/10^{5})^{100} = 0.99995^{100}

("approximately" because I've ignored the fact that a drawn ticket will not be replaced; but with such a large number of tickets the impact of this will be small).

Therefore the chance of you winning is p = 1 - 0.99995^{100}

$${\mathtt{p}} = {\mathtt{1}}{\mathtt{\,-\,}}{{\mathtt{0.999\: \!95}}}^{{\mathtt{100}}} \Rightarrow {\mathtt{p}} = {\mathtt{0.004\: \!987\: \!645\: \!188\: \!015\: \!9}}$$

or p ≈ 0.005

Alan
Sep 16, 2014

#2**+8 **

Best Answer

i have 5 tickets for a lottery that contains a total of 100.000 tickets. 100 tickets are drawn, what are the chances of me winning?

Im splitting them into 100 winning and 99900 losing tickets

1-P(5lose)

1-(99900C5/100000C5)

Very close to 5/1000 = 1/200

That's what I think anyway.

Melody
Sep 16, 2014

#3**0 **

Alan, you beat me! Mine is exact I think.

Not many calculators can deal with such large numbers though.

Melody
Sep 16, 2014