[LaserPineapple]

> We pick one of the three coins at random, toss it 300 times and count the number of heads.

This is the procedure. One of the coins is chosen, and that same coin is flipped 300 times. Conditional on which coin was chosen, the number of heads is Binomial, so the unconditional distribution is a mixture of three Binomials.

[em500]

But a few lines later, it states

> This time, however, each time we take a sample we might be tossing any of the three different coins.

which is a different procedure