Friday 5 June 2015

Hannah's Sweets

Quite a few GCSE students were stumped by a question about Hannah's sweets on yesterday's higher tier Edexcel paper.

The question was:

Hannah has 6 orange sweets and some yellow sweets.
Overall, she has n sweets. She takes one sweet from the bag and then another.
The probability of her taking 2 orange sweets is 1/3.
Prove that: 

The question is not actually that difficult if you remember how tree diagrams work.

When Hannah first takes a sweet there are 6 orange sweets out of n, so the probability of her choosing orange is 6/n.

When she chooses her second sweet there are now only 5 orange (if she chose orange the first time) out of a total of n-1 sweets.
You multiply the probabilities along the branches of a tree diagram, so

 Multiplying the 2 fractions on the left gives:

Cross-multiplying gives: