Sweet ignorance

The children in the UK have been moaning about an exam question, which was as follows:

There are n sweets in a bag. 6 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.

equationsThe question isn’t hard. You just take the odds of the first sweet being orange, and then multiply that by the odds of the second sweet being orange, and that is 1 in 3. It is 3 lines of calculation.

But what I think might be quite hard is doing it if you don’t have a piece of paper, but merely a computer. I guess if I spent long enough messing around with text boxes or whatever in Word I would be able to reproduce these simple equations, but it would take me quite a while (far longer than actually solving the problem).

Maybe the children know how to do this stuff using their computers. But at 16 years old, they really shouldn’t be complaining about such a simple question as a matter of the maths. They weren’t even asked here to solve the quadratic equation, which could easily be solved by factorisation; the equation can be rewritten as:

(n – 10) * (n + 9) = 0

and so since either n – 10 has to equal 0, or n + 9 has to equal 0, so n has to equal either 10 or -9. The latter is nonsensical, so the answer is that there were 10 sweets in the bag. Is it really too much to ask that children learning maths should be able to do this sort of thing by the time they are 16? Or has the education system becomes so dumbed down that only a University student might be asked such a thing?

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One response to “Sweet ignorance

  1. Pingback: Sweet impossibility | phenell

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