On Fri, 05 Jun 2015 15:01:13 +0100, Tim Watts wrote:

GCSE's getting harder causes Paul Dacre's head to explode.

or

"Slightly hard" GCSE Maths Question causes outrage...


http://www.bbc.co.uk/news/education-33017299



The actual question was:

Hannah has 6 orange sweets and some yellow sweets. Overall, she has n
sweets.
The probability of her taking 2 orange sweets is 1/3.

Prove that: n^2-n-90=0

That's actually quite a cunning stinker. What makes it such a stinker is
the reliance on inferring the true nature of the probability statement
which needs very close scrutiny to determine that what is actually meant
is defining the probability of blindly extracting the first *two* sweets
from the bag. It matters not as to whether both sweets are collected in a
single grab or one by one, the resulting probability remains the same.

The probability of randomly picking orange sweets at each successive
trial drops each time until there are no more orange sweets left where it
becomes zero in the extremely improbable event that all picks succeeding
in selecting an orange sweet until no more were left to pick.

My initial guess for n was 18 (6 orange sweets outnumbered 2 to 1 by 12
yellow sweets to give the initial one in three chance I'd naively
assumed). It was only the fact that 18^2 equals a whopping 324 that made
me pause for thought and take another 'guess'. I tried n=12 before
realising it had to 10. Only then was I able to determine that the actual
probabilities of the first two picks being an orange sweet would be 60%
(6 in 10 chance) for the first then 55.55555555% (5 in 9 chance) for the
second giving an overall probability of 60% of 55.55555% = to 33.333333%
or one third.

I'd say that 'guessing' likely values for n in this case (integer values
only) would be considered an entirely legitimate approach to take in
order to determine the value of n which can be the only value that also
allows the stated one in three probability to be true.

I'm sure there must be a more strict formula involving the use of square
roots but, since the algorithm for calculating a square root also
involves the use of 'guessed' values in an iterative process to swiftly
calculate a value of sufficient accuracy, I think the guessing method is
still entirely legitimate nonetheless. :-)


--
Johnny B Good