The following question is from a Basic Statistics course on Coursera:
In a shop, people can take chewing gum from a dispenser on the right, or the left. The dispenser on the right has 7 packets of mint gum, and 3 packets of fruit gum, and the dispenser on the left has 7 packets of mint gum and 7 packets of fruit gum.
Someone buys a packet of mint gum - what is the probability that they took this packet from the right dispenser?
You are required to calculate the following:
- P(mint | right)
And then apply Bayes law to find P(right | mint).
My initial thinking
My initial approach was to create a data matrix, convert to probabilities (divide by 24 - total number of packets) and simply use joint and marginal probabilities.
But the answer provided is:
- P(mint | right) = 7/10 (clearly ignore the left dispenser)
- P(right) = 0.5 (clearly assuming there is 50/50 chance between dispensers)
- P(mint) = 14/24 (seem to be making use of 24 packets, ie marginal of both right and left dispensers)
I can kind of understand why
P(mint | right) = 7/10.
I can also (kind of) understand why there's 50/50 chance for dispenser selection.
But the two seem to be based on dispenser-based probabilities rather then packet probabilities.
So how come that we use 24 (total amount of packets) when calculating
It seems that sometimes a dispenser-based approach is taken, sometimes a packet-based approach.
Does it smell?
Finally, am I wrong to feel this is not the greatest of questions?