# Hannah and her sweets

Apparently students in the UK have been protesting against the following question on a GCSE math exam (see e. g. coverage at *The Guardian*):

There are n sweets in a bag. Six of the sweets are orange. The rest of the sweets are yellow. Hannah takes a random sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag. She eats the sweet. The probability that Hannah eats two orange sweets is 1/3. Show that n²-n-90=0.

The probability that the first sweet is orange is $latex 6/n$. Now there are five orange sweets left out of $latex n-1$, so the probability that the second sweet is orange, assuming that the first one is, is $latex 5/(n-1)$. Therefore we need to solve $latex (6/n) times (5/(n-1)) = 1/3$. Multiplying it out gives

$latex {30 over n(n-1)} = {1 over 3}$

and we can…

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Posted on June 5, 2015, in Uncategorized. Bookmark the permalink. Leave a comment.

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