Questions: A video game allows a player to create a clothes outfit by choosing 1 of 3 hats, 1 of 2 shirts, and 1 of 4 pants. The game has two players. What are the chances that both players create the same clothes outfit? (A) 1 in 100 (B) 1 in 6 (C) 1 in 24 (D) 1 in 64

Solution Steps

To determine the chances that both players create the same clothes outfit, we need to calculate the total number of unique outfits possible and then find the probability that both players independently choose the same outfit.

1. Calculate the total number of unique outfits by multiplying the number of choices for each clothing item.
2. Since each player chooses an outfit independently, the probability that both players choose the same outfit is the reciprocal of the total number of unique outfits.

To determine the total number of unique outfits, we multiply the number of choices for each clothing item: \[ \text{Total Outfits} = \text{Number of Hats} \times \text{Number of Shirts} \times \text{Number of Pants} \] Given: \[ \text{Number of Hats} = 3, \quad \text{Number of Shirts} = 2, \quad \text{Number of Pants} = 4 \] Thus: \[ \text{Total Outfits} = 3 \times 2 \times 4 = 24 \]

Since each player chooses an outfit independently, the probability that both players choose the same outfit is the reciprocal of the total number of unique outfits: \[ \text{Probability} = \frac{1}{\text{Total Outfits}} = \frac{1}{24} \]

Final Answer