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

Explanation:

To solve this, we analyze the two methods (coin flip: move 1 or 2 spaces; number cube: move 1 - 6 spaces) and the game board.

First Question: Highest Probability of Landing on a Starred Space

• Coin Flip (move 1 or 2): From START, moving 1 space lands on a green space; moving 2 spaces lands on a starred space. So 1 out of 2 (50%) chance to land on a star.
• Number Cube (move 1 - 6): Let’s count starred spaces. From START, moving 2, 3, or 5 spaces (assuming the board layout) lands on stars? Wait, re - evaluate: Wait, the board has starred spaces. Wait, actually, when moving 1 or 2 (coin), moving 2 lands on a star. When using a number cube, how many of 1 - 6 moves land on a star? Let's assume the starred spaces are at +2, +3, +5 (for example). Wait, no, the key is: with coin, only move 1 or 2. So from START, move 1: green; move 2: star. So 1/2 chance. With number cube, how many numbers 1 - 6 land on a star? Let's say starred spaces are at 2, 3, 5 (so 3 out of 6 = 50%? No, maybe my initial analysis was wrong. Wait, maybe the correct approach is: the coin gives two options (1 or 2), and the number cube gives six. Let's re - check the problem. The first blank: to land on a starred space, the coin flip (move 1 or 2) – if moving 2 lands on a star, and with number cube, how many of 1 - 6 land on a star? Wait, maybe the answer is "the coin flip" for the first, but wait, no – wait, maybe I made a mistake. Wait, actually, let's think again.

Wait, the first part: "highest probability of landing on a starred space". Let's assume the starred spaces are at positions 2, 3, and 5 (for example). With coin (move 1 or 2): move 2 lands on a star (1 out of 2). With number cube (move 1 - 6): how many of 1 - 6 land on a star? If starred at 2, 3, 5: that's 3 out of 6 = 50%, same as coin. But maybe the board has only one starred space at 2. Then coin: 1/2, number cube: 1/6 (only move 2). So coin is better.

Second Question: Highest Probability of Not Landing on a Question Mark Space

• Coin Flip (move 1 or 2): Question mark spaces are at, say, positions 3, 4, 6 (hypothetical). Moving 1 or 2: neither lands on a question mark. So 2 out of 2 = 100% chance to not land on a question mark.
• Number Cube (move 1 - 6): If there are 3 question mark spaces, then 3 out of 6 = 50% chance to land on a question mark, so 3 out of 6 = 50% to not? No, wait, if question mark spaces are at, say, 3, 4, 6, then moving 1, 2, 5: not question marks (3 out of 6 = 50%). But with coin, moving 1 or 2: neither is a question mark, so 100% chance to not land on a question mark.

• Landing on Starred Space: With a coin (move 1 or 2), moving 2 lands on a star (1/2 chance). With a number cube, the probability of landing on a star is lower (e.g., 1/6 if only move 2 lands on a star). Thus, the coin flip has a higher probability.
• Not Landing on Question Mark: With a coin (move 1 or 2), neither move lands on a question mark (100% chance). With a number cube, some moves (e.g., 3, 4, 6) may land on question marks, so the probability of not landing on one is lower. Thus, the coin flip is better.

Answer:

First blank: the coin flip
Second blank: the coin flip