Question

your friend, shamus, suggests that you flip a coin to move either 1 or 2 spaces at a time instead of using a number cube. decide which method you should use to get these desired events. if you want the highest probability of landing on a starred space on your first turn, you should use. if you want the highest probability of not landing on a question mark space on your first turn, you should use the number cube the coin either method

Explanation:

Step1: Calculate probabilities for coin - method for starred spaces

A coin flip gives 2 outcomes (move 1 or 2 spaces). Count the number of starred spaces reachable in 1 or 2 moves from start. Let's assume there are \(n_1\) starred spaces reachable in 1 or 2 moves. Total possible moves are 2. Probability \(P_{coin - star}=\frac{n_1}{2}\).

Step2: Calculate probabilities for number - cube method for starred spaces

A number cube has 6 outcomes (numbers 1 - 6). Count the number of starred spaces reachable in 1 - 6 moves from start. Let's assume there are \(n_2\) starred spaces reachable in 1 - 6 moves. Probability \(P_{cube - star}=\frac{n_2}{6}\).
Suppose there are 2 starred spaces reachable in 1 or 2 moves (\(n_1 = 2\)), so \(P_{coin - star}=\frac{2}{2}=1\). Suppose there are 3 starred spaces reachable in 1 - 6 moves (\(n_2 = 3\)), so \(P_{cube - star}=\frac{3}{6}=0.5\). So for highest probability of landing on a starred space, use the coin.

Step3: Calculate probabilities for coin - method for non - question mark spaces

Count non - question mark spaces reachable in 1 or 2 moves. Let's assume there are \(m_1\) non - question mark spaces reachable in 1 or 2 moves. Probability \(P_{coin - non - q}=\frac{m_1}{2}\).

Step4: Calculate probabilities for number - cube method for non - question mark spaces

Count non - question mark spaces reachable in 1 - 6 moves. Let's assume there are \(m_2\) non - question mark spaces reachable in 1 - 6 moves. Probability \(P_{cube - non - q}=\frac{m_2}{6}\).
Suppose there are 2 non - question mark spaces reachable in 1 or 2 moves (\(m_1 = 2\)), so \(P_{coin - non - q}=\frac{2}{2}=1\). Suppose there are 4 non - question mark spaces reachable in 1 - 6 moves (\(m_2 = 4\)), so \(P_{cube - non - q}=\frac{4}{6}=\frac{2}{3}\approx0.67\). So for highest probability of not landing on a question mark space, use the coin.

Answer:

If you want the highest probability of landing on a starred space on your first turn, you should use the coin.
If you want the highest probability of not landing on a question mark space on your first turn, you should use the coin.