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Thomas rolls two dice, one is 6-sided and one is 4-sided. What is the probability that Thomas gets. Number on the 6-sided die that is smaller than the number on the 4-sided die

2 Answers

1 vote

Final answer:

To determine the probability, all possible outcomes of the two dice are considered, and all pairs where the 6-sided die has a smaller number than the 4-sided die are counted. There are 6 such favorable outcomes out of a total of 24 possible outcomes, resulting in a probability of 1/4 or 25%.

Step-by-step explanation:

The question asks for the probability that the number rolled on a 6-sided die is smaller than the number rolled on a 4-sided die. The 6-sided die has faces labeled {1, 2, 3, 4, 5, 6} while the 4-sided die has faces labeled {1, 2, 3, 4}. To find the probability, we consider all possible outcomes of rolling the two dice together, which forms a sample space. The 6-sided die and the 4-sided die are independent events, so the total number of outcomes is the product of the number of outcomes for each die, which is 6*4 = 24 outcomes.

Step-by-step explanation:

  • Determine the sample spaces: S₆ = {1, 2, 3, 4, 5, 6} for the six-sided die and S₄ = {1, 2, 3, 4} for the four-sided die.
  • Count all possible pairs (x,y) where x is from S₆ and y is from S₄.
  • Identify all pairs where x < y.
  • Count the number of pairs where x < y.
  • Divide the count of favorable pairs by the total number of pairs (24) to calculate the probability.

The favorable pairs, where the number on the 6-sided die is smaller than that on the 4-sided die, are: (1,2), (1,3), (1,4), (2,3), (2,4), and (3,4). That gives us 6 favorable outcomes out of 24 possible outcomes, which gives us a probability of 6/24 = 1/4 or 0.25.

User DarkRob
by
8.1k points
6 votes

Answer:

1/4

Step-by-step explanation:

If the number on the 4-sided die is a "1", the probability is 0/6.

If the number on the 4-sided die is a "2", the probability is 1/6.

If the number on the 4-sided die is a "3", the probability is 2/6.

If the number on the 4-sided die is a "4", the probability is 3/6.

Each of the sides of the 4-sided die has a 1/4 probability of being rolled.

The total probability is therefore:

P = (1/4) (0/6) + (1/4) (1/6) + (1/4) (2/6) + (1/4) (3/6)

P = 0/24 + 1/24 + 2/24 + 3/24

P = 6/24

P = 1/4

User Patrick Berkeley
by
8.3k points

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