Probability question (1 Viewer)

[chrisso23]

I came across this the other day, and was wondering if someone could help me.
in a jackpot lottery, 1000 numbers are drawn from a barrel containing the 60,000 ticket numbers available. After all 1000 prize winning numbers are drawn they are returned to the barrel and a jackpot number is drawn. If the jackpot number is the same as one of the 1000 numbers that have already been selected, then the additional jackpot prize is won.
A) calculate the prob. that the jackpot prize will be won in a given game.
B) Calculate the prob that the jackpot prize will be won at least once in 12 independant games.
C) the jackpot prize is initially $5000 and it increases by $5000 each time the prize is not won. Calculate the prob. that the jackpot will exceed $100000 when it is finally won.

 

[Lazarus]

(A)
<pre>P(winning jackpot) = 1000/60000
= 1/60</pre>
(B)
<pre>P(jackpot won at least once) = 1 - P(never winning jackpot)
= 1 - (59/60)¹²
= 1 - 0.8173...
~ 0.18 (2 dec. places)</pre>
(C)
<pre>NB: 100000/5000 = 20
P(jackpot prize > $100k) = P(jackpot not being won > 20 times)
= (59/60)²¹
= 0.7026...
~ 0.70 (2 dec. places)</pre>

 

[Pythagoras]

There was a similar problem in the 1995 3Unit HSC paper. Just the numbers changed for your problem. Lazarus' solution is correct.