Probability

Total outcomes = 36. Favorable outcomes for same even number: (2,2), (4,4), (6,6). Total 3 outcomes. Probability = 3/36 = 1/12.

The minimum sum of two dice is 1+1=2. Therefore, it is impossible to get a sum of 1.

A standard six-sided die has outcomes {1, 2, 3, 4, 5, 6}. Among these, 4 and 6 are composite numbers, while 2, 3, and 5 are prime, and 1 is neither prime nor composite.

A die has 6 faces: {1, 2, 3, 4, 5, 6}. The numbers less than or equal to 5 are {1, 2, 3, 4, 5}. There are 5 such outcomes. The probability is 5/6.

Each individual ball is a possible outcome, and the bag contains 3 + 5 + 4 = 12 balls. Therefore, the total number of outcomes is 12.

Each coin toss has 2 outcomes. For 4 tosses, the total number of outcomes is 2^4 = 16.

A fair die has outcomes {1, 2, 3, 4, 5, 6}. The multiples of 3 are {3, 6}. The probability is 2/6 = 1/3.

A standard die has 6 faces, so there are 6 possible outcomes when thrown.

A standard die has six faces: 1, 2, 3, 4, 5, 6. The even numbers are 2, 4, and 6, which are three outcomes out of six, resulting in a probability of 3/6 or 1/2.

A standard die has 6 faces. The probability of rolling a specific number like 4 is 1/6.

Factors of 5 are 1 and 5. The die outcomes are {1, 2, 3, 4, 5, 6}. Outcomes that are NOT factors of 5 are {2, 3, 4, 6}. There are 4 such outcomes out of 6. Probability = 4/6 = 2/3.

A fair 6-sided die has outcomes {1, 2, 3, 4, 5, 6}. The probability of getting a 3 is 1/6. The probability of not getting a 3 is 1 - 1/6 = 5/6.

A doublet occurs when both dice show the same number. There are 6 doublets (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6) out of 36 total possible outcomes. The probability is 6/36, which simplifies to 1/6.

The prime factors of 3 are just {3}. A die has {1, 2, 3, 4, 5, 6}. The probability of rolling a 3 is 1/6.

Total probability is 1. If P(red) = a/b, then P(white) = 1 - a/b = (b-a)/b.