When a pair of six sided dice is rolled , each with faces numbered 1 to 6,is rolled once, what is the probability that the result is either 3 and 4 or a 5 and a prime number?

In probability, there are hint clues that you must be vigilant of. When it tells you to find the probability of event 1 'or' event 2, you must ADD their individual probabilities. When it tells you to find the probability of event 1 'and' event 2, you must MULTIPLY their individual probabilities. 

Now, you have two dices. You are asked to find the probability of getting a face of 3, 4 or 5. The probability of each face of a dice is 1/6, because there are a total of 6 faces. When you use two dices, it becomes 2/12 or still 1/6. So, the total probability of getting either 3, 4 or 5 is: 1/6 + 1/6 + 1/6 = 1/2. However, you still have to multiply this with the total probability of getting a prime numbers which are 1, 2, 3 and 5. Thus, 1/6 + 1/6 + 1/6 + 1/6 = 2/3

Hence, the total probability would be 1/2 * 2/3 = 1/3 or 33%