Financial Risk Manager Part 1
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In a game, a coin is flipped. If the coin is heads, the player rolls one die. If the coin turns up tails, the player rolls two dice and the player moves their playing piece the number of spots shown on the die or dice. What is the probability of moving less than 3 spaces on a turn?
Other
Community
NNikitesh
A
3%
B
5%
C
8%
D
18%
Explanation:
The probability of moving less than 3 spaces is calculated as follows:
Step 1: Define events
- Coin flip: Heads (H) with probability 1/2, Tails (T) with probability 1/2
- If H: Roll 1 die → possible outcomes: 1-6
- If T: Roll 2 dice → possible outcomes: 2-12
Step 2: Calculate P(1)
- P(1|H) = 1/6 (only way to get 1 with one die)
- P(1|T) = 0 (impossible to get 1 with two dice)
- P(1) = P(1|H) × P(H) + P(1|T) × P(T) = (1/6) × (1/2) + 0 × (1/2) = 1/12
Step 3: Calculate P(2)
- P(2|H) = 1/6 (only way to get 2 with one die)
- P(2|T) = 1/36 (only way: (1,1) with two dice)
- P(2) = P(2|H) × P(H) + P(2|T) × P(T) = (1/6) × (1/2) + (1/36) × (1/2) = 1/12 + 1/72 = 7/72
Step 4: Calculate P(<3)
- P(<3) = P(1) + P(2) = 1/12 + 7/72 = 6/72 + 7/72 = 13/72 ≈ 0.1806
- Convert to percentage: 13/72 × 100% ≈ 18.06% ≈ 18%
Therefore, the probability of moving less than 3 spaces is 18%.
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