Write down all the outcomes went to dice is thrown also find the proba...
Outcomes of throwing a dice:
- 1, 2, 3, 4, 5, 6
Outcomes of sum of two dice:
- 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Outcomes of product of two dice:
- 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36
Probability of product of two dice is equal to sum of two dice:
- To find the probability of the product of two dice being equal to the sum of the two dice, we need to identify the outcomes that satisfy this condition. The outcomes where the product is equal to the sum are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (3, 3), (4, 4), (5, 5), (6, 6), (4, 4), and (6, 6). There are a total of 12 outcomes that satisfy this condition.
Calculating the probability:
- Total number of outcomes when two dice are thrown = 6 * 6 = 36
- Probability = Number of favorable outcomes / Total number of outcomes
- Probability = 12 / 36 = 1/3
Therefore, the probability of the product of two dice being equal to the sum of the two dice is 1/3.