AP BIOLOGY

Detailed explanation-1: -When two dice are rolled, there are now 36 different and unique ways the dice can come up. This figure is arrived at by multiplying the number of ways the first die can come up (six) by the number of ways the second die can come up (six). 6 x 6 = 36. This graphic shows this very nicely.

Detailed explanation-2: -Note that there are 36 possibilities for (a, b). This total number of possibilities can be obtained from the multiplication principle: there are 6 possibilities for a, and for each outcome for a, there are 6 possibilities for b. So, the total number of joint outcomes (a, b) is 6 times 6 which is 36.

Detailed explanation-3: -The number of total possible outcomes is equal to the total numbers of the first die (6) multiplied by the total numbers of the second die (6), which is 36. So, the total possible outcomes when two dice are thrown together is 36.

Detailed explanation-4: -Why do we know, without listing them all, that there are 36 outcomes when two dice are rolled? We can view the outcomes as two separate outcomes, that is, the outcome of rolling die number one and the outcome of rolling die number two.

Detailed explanation-5: -We can take the number of combinations (30) and divide it by the size of the sample space (36), resulting in a probability of 5/6.