[Fraser has won Competition Three]
OK. I have a copy of Evolution: How We And All Living Things Came To Be by Daniel Loxton as a prize for Competition Three. This is the best prize yet and will go to the SF boy who best answers and explains the following problem.
Mr Bishop has an opaque bag in which he says there is either a packet of Fruit Pastilles or a packet of Wine Gums. He puts into the bag a packet of Fruit Pastilles whilst you are watching. He then reaches in and chooses one of these two packets at random from the bag. His choice turns out to be a packet of Fruit Pastilles which he says he will give to you if you can answer the following question. What is the probability that the remaining packet in the bag is also Fruit Pastilles?
If you can work out and explain the answer to this question please either use the comments section below or email me with your explanation. I will not post answers that do not come with explanations, but I will post questions and any responses I might choose to give.
Good Luck!
The answer is 2/3. There are four possible outcomes when Mr Bishop draws the first packet from the bag. To help describe it, let’s call the unknown packet of sweets either Fruit Pastillesx or Wine Gumsx. The four possible outcomes are that Mr Bishop draws out…
- Fruit Pastilles leaving Fruit Pastillesx in the bag.
- Fruit Pastilles leaving Wine Gumsx in the bag.
- Fruit Pastillesx leaving Fruit Pastilles in the bag.
- Wine Gumsx leaving Fruit Pastilles in the bag.
Assuming Mr Bishop can be trusted to tell the truth (which is why I chose him!) then each of the above outcomes is equally possible. Once he has drawn Fruit Pastilles out of the bag though, the number of possible outcomes decreases to three and Fruit Pastilles figure in two of them so the probabillity is 2/3.
Fraser’s explanation was good enough I decided to win him the prize. Well done!
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