The final flavor to appear

Question

A drink brand has 5 equally likely flavors, one printed under each cap, independent per bottle. You buy bottles until you have seen all five flavors. One flavor is mango.

What is the probability that mango is the last new flavor to appear?

Accepted Answer

Mango is drawn with exactly the same probability as every other flavor on every bottle, so its label gives it no special tendency to come early or late. The five flavors are interchangeable. By symmetry, each flavor is equally likely to be the last one seen for the first time, so P(	ext{mango is last}) = \frac{1}{5} = 0.2. Takeaway. With n equally likely types, any named type is the last to appear with probability \frac{1}{n}; here \frac{1}{5}.

The final flavor to appear

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