A Mochi Problem with Unequally Likely Flavors

You are given a box of 10 mochis with three flavors: 5 Strawberry (S) 🍓, 3 Coconut (C) 🥥, and 2 Matcha green tea (M) 🍵.

You randomly take a mochi, and a genie refills the box with a mochi of the same flavor. This process is repeated 3 times.

Let the outcome of the experiment be a sequence of three mochis (e.g., $(S, C, M)$).

Questions:

• (1 point) What is the probability of getting 3 Matcha mochis, the rarest flavor, in a row?
• (1 point) What is the probability of getting exactly 2 Matcha mochis in the 3 draws?
• (1 point) What is the probability of getting at least 1 Matcha mochi in the 3 draws?
• (1 point) Suppose a “winning sequence” is defined as any sequence of all three flavors. What is the probability of drawing a “winning sequence”?

Please send your solution to me via email. Good luck!