rolling a number cube and tossing two coins
There are a few different possible ways to interpret this prompt, so here are a few examples of problems that could be related to rolling a number cube and tossing two coins:
1. You roll a standard number cube (with numbers 1-6) and toss two fair coins. What is the probability that the number on the cube is even and both coins show heads?
2. You roll a number cube that has a 1 on two sides, a 2 on two sides, and a 3 on two sides. You also toss two coins, one of which is fair and the other of which is weighted to come up heads 75% of the time. What is the probability that the cube shows a 1 and the fair coin shows heads, or the cube shows a 2 and the weighted coin shows heads?
3. You are playing a game with a friend where you take turns rolling a number cube and tossing two coins. Each time you roll the cube and toss the coins, you earn points based on the following rules:
- If the cube shows 1 or 4 and both coins show heads, you earn 10 points
- If the cube shows an odd number and one coin shows heads and one shows tails, you earn 5 points
- If the cube shows a multiple of 3 and both coins show tails, you lose 3 points
- In all other cases, you earn 1 point.
Your friend goes first and rolls a 6 and gets one heads and one tails on the coins. You roll a 3 and get two tails on the coins. What is the score after these two rounds?