a probability question - past HSC (1 Viewer)

[haboozin]

Hey,

I just dont think they are right with their answer.

1995 Q5biii

.....
In a jackpot lottery, 1500 numbers are drawn from a barrel containing 100,000 tick numbers available.
After all the 1500 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 1500 numbers that have already been selected, then the addictional jackpot prize is won

THe probability that the jackpot prize is won in a given game is
p=1500/100000 = 0.015

(so bionomial probability)

iii,
The jackpot prize is initially 80000 and it increases by 80000 each time the prize is not won
calculate the probability that the jacpot prize will exceed $200,000 when it is finally won.

ok so obviously its x + 1 = 200,000/8000
x= 24
but it must exceed
so x= 25

but this question says "before its actually won"
so shouldn't we assume it is won after the 26th time

so we get 26c1 x 0.015x 0.985^25
?
MANSW answers say its 0.985^25 which only answers if it is not won after the 25th time.

 

[serge]

its initially $8000

You've already written the right thing
that 25 times exceeds 200,000

"but it must exceed
so x= 25"

there's no need to make it x=26 times

 

[haboozin]

its initially $8000

You've already written the right thing
that 25 times exceeds 200,000

"but it must exceed
so x= 25"

there's no need to make it x=26 times

but the question says when the prize is finally won..

they only answered it for when the prize hasnt been won after the 25th time.
Nothing to say that the prize will be won.

 

[noah]

The probability that the prize will never be won limits to zero therefore the probability that it will be won eventually after its 25th time will be equal to the probability that it will not be won on the first 25 times.

Your approch with binomial probability is wrong even if the question were "what is the probability that the game is won on the 26th time and not before". By using the binomial coefficiant you are saying that it could be won on any of the first 26 games not on the 26th game.

 

[HayleeKate]

agreed that its 25... look at the question this way:
for the jackpot to exceed $200 000, it must be not won 25 consecutive times, (and then it doesnt matter when its won after that, it will be more than $200000), so whats the probability that it will be not won 25 consecutive times? 0.985^25

 

[currysauce]

ok so obviously its x + 1 = 200,000/8000
x= 24
but it must exceed
so x= 25

can i ask, why is obvious that x+1 = such and such , makes no sense to me

 

[HayleeKate]

its x + 1, because you have the original $8000 (the +1) plus each additional $8000 (x)
so, (x + 1)8000 = 200 000
will give how many times the jackpot must be missed to REACH 200 000,
x + 1= 200000/8000
x=24, so after the jackpot is missed 24 times, the sum reaches 200 000,
then, the next time it EXCEEDS 200 000.
Does that clear it up, with the explanation in there?