Each bag ontains exactly 8 cubes. Some bags contain 4 cubes of each colour, some

Question

Each bag ontains exactly 8 cubes. Some bags contain 4 cubes of each colour, some contain 6 red cubes and 2 green cubes, and some contain 2 red cubes and 6 green cubes. Your job is to guess – with as high a degree of accuracy as you can – the contents of each bag.

Chosen strategy: Remove three cubes, look at them, put them back in the bag, then repeat this once more.

Discuss the probability of guessing the correct set of cubes in each bag and determine a success rate for guessing the contents. Discuss faults with the strategy and possible improvements.

Explanation / Answer

Lets consider a Bag with 4 Red and 4 Green cubes, in this case below table gives the possible cominations of drawing 3 cubes and its probabilities

Lets consider a Bag with 2 Red and 6 Green cubes, in this case below table gives the possible cominations of drawing 3 cubes and its probabilities

Lets consider a Bag with 6 Red and 2 Green cubes, in this case below table gives the possible cominations of drawing 3 cubes and its probabilities

From the able 3 tables we see when the outcome is 1R+2G or 2R+1G, probability that it is from 4R+4G bag is 0.4285 and from 2R+6G or 6R+2G is 0.5371. This is not much different. Whereas if 3R it is easy to say that it is from 6R + 2G Bag, because probability of getting this is very high than getting this outcome with 4R+4G bag.

In this stategy, fault will occur when there are 1R+2G or 2R+1G will be the outcome.

Possible outcome 3R 3G 2R+1G 1R+2G Number of combinations 4 4 24 24 Probability 0.071429 0.071429 0.428571 0.428571

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