What operation is used when calculating the probability that 2 events will happen and Find the theoretical probability of rolling a total of 7 as a sum of two dices?

Answer 1

If the two events are unrelated, as they are in rolling two dice or one die twice, simply multiply the probabilities together. However, you also have to consider the permutations involved in rolling dice and realize that there is more than one way to roll a particular sum.

There are 36 permutations of rolling two dice. Of these, exactly one has a sum of two, the the probability of rolling a sum of two is 1 in 36, or about 0.02778. You simply multiply 1 in 6 by 1 in 6, getting 1 in 36. In the case of rolling a sum of seven, there are exactly six permutations, 1+6, 2+5, 3+4, 4+3, 5+2, and 6+1, so the probability of rolling a sum of seven is 6 in 36, or 1 in 6, or about 0.1667.

Another example is rolling pairs, such as two's or three's. The probability of rolling "something" on one die is 1 in 1, while the probability of matching it on the second die is 1 in 6, so you multiply (1 in 1) by (1 in 6) to get a probability of rolling a pair of 1 in 6, or about 0.1667.

More useful towards understanding this concept is a deck of 52 cards. The probability of drawing an Ace is 4 in 52, or 1 in 13, or about 0.07692. The probability of drawing two Ace's is (4 in 52) times (3 in 51), or 12 in 2652, or 1 in 221, or about 0.004525. In this case, the two events are related, because the occurrence of the first event affects the probability of the second event, so you need to consider the calculation carefully.