G C S E More Sweets

[kuiperbelt]

There are N sweets in a bag. Eight of the sweets are red. The rest of the sweets are green.
Jack takes a random sweet from the bag. He eats the sweet. Jack then takes at random another
sweet from the bag. He eats that sweet too. The probability that Jack eats two red sweets is 20%
Find how many sweets were in the bag to begin with? Must show your working.

[ZebuSanctuary]

Probability of picking first red sweet is 8/N
Probability of selecting second red sweet is 7/(N-1)
Probability of getting 2 consecutive red sweets is 20% or 1/5

Thus 8/N x 7/(N-1) = 1/5;

56/N(N-1) =1/5 -----> 56 x 5 = N(N-1) which yields;

280 = N² - N or N² - N - 280 = 0

Eq is quadratic in N. At a guess 17 or 18 sweets let us see;

18² - 18 - 280 =0 -----> (26)
17² - 17 - 280 = 0 ------> (-8)

Answer approx 17.2 Sweets.

[ClareTG0ld]

I can't see an error in Zebu's working, so on that basis the answer is that this problem is impossible, since by definition you can only have a whole number of sweets.

Presumably somewhere along the line, there's a typo. The most plausible, to me, is that there were meant to be seven red sweets initially, leading to 15 total sweets (as 7/15*6/14 = 1/5).

[Gizmonster]

I got the same solution as Zebu:
N² - N - 280 = 0
.... when I solved it, I realised it wasn't a whole number, so I assumed I'd made a mistake and didn't post my answer .... surely common sense says the answer should be a whole number ??

[bobbinwales]

Yes if its an old gcse question there's an error here....I remember it in the paper.answer was 11 I remember?? So numbers wrong here?

[bobbinwales]

I was thinking of this Hannah one

[bobbinwales]

https://www.google.com/search?q=gcse+sweets+probability+quesyion&oq=gcse+sweets+probability++quesyion&aqs=chrome..69i57j33i10i160l3.13122j0j4&client=ms-android-samsung-gj-rev1&sourceid=chrome-mobile&ie=UTF-8#imgrc=pWqtF4Opl0kdnM&;lnspr=W10=

[ClareTG0ld]

Yeah, that one I remembered, I think it was stumping a lot of people at the time, presumably because probability isn't taught properly (or just enough people on twitter hadn't paid attention) -- or, perhaps, because it seems to jump to a quadratic equation and maybe people who "compartmentalise" maths too much didn't realise that it jumps out of applying what they *did* know about probability, and panicked in the face of an apparently unrelated question.

In any case, the answer has to be a whole number, so since at least two people independently have found that it does not work, something went wrong.

[kuiperbelt]

Grandson tells me the answer is 17. Obviously the question is flawed. He will raise query with teacher or TA. He is grateful for the method on how to tackle the problem!!

Amazing how you got the answer (17.2) without resorting to Quadratic formula!!

[ZebuSanctuary]

//the answer (17.2) without resorting to Quadratic formula!!//

When the answer expected, an integer in this case, one should not have to resort to the messy quadratic formula. Factorising more than suffices.

[bobbinwales]

The 17.2 was just a calculated estimate I reckon based on the fact that (copied from ZebuSanct's answer)
18² - 18 - 280 =0 -----> (26)
17² - 17 - 280 = 0 ------> (-8)
So as 0 is approx 1/4 - 1/5 of the way between 26 and -8 then the answer is about the same roughly between 7 and 8 so 7 is a good shout.
I think?