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# 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?

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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
+94118
+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
+27229
+5

I asume the total number of tickets is 105

The chance that none of your 5 is drawn is approximately (1-5/105)100 = 0.99995100

("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 - 0.99995100

\$\${\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
+94118
+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
#3
+94118
0

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

Not many calculators can deal with such large numbers though.

Melody  Sep 16, 2014
#4
+27229
0

Yes, your answer is exact Melody.  I noted in my answer that mine was approximate; but it was a quick way of doing it!

Alan  Sep 16, 2014
#5
+94118
0

Yes it was a good way.   I had to go to Wolfram|Alpha to find a calc that would play ball.

Melody  Sep 16, 2014