An ordinary fair die is a cube with the numbers through on...

An ordinary (fair) die is a cube with the numbers through on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event A: The sum is greater than 6. Event B: The sum is divisible by 5 or 6 (or both). Round your answers to two decimal places.

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Transcript

00:01 Okay, if i throw two dice or if i throw one die twice and add up the scores, my sample space will be between 2 and 12.

00:11 My lowest score possible is a 1 on the first die plus a 1 on the second die.

00:17 The highest score will be 12, 6 on both dice.

00:24 Getting a 3 more chance, 1 plus 2 or 2 plus 1.

00:28 Getting a 4, 1 plus 3, 3 plus 1, or 2 and 2, 5, 1 and 4 and 1, 2 plus 3, getting more common as we go up.

00:45 1 and 5, 5 and 1, 2 and 4 and 2, 3 and 3.

00:56 7 is the most common, you see why in the moment.

01:00 1 plus 6, 6 plus 1, 2 plus 5.

01:05 5 plus 2, 4 plus 3, 3 plus 4.

01:11 There are 6 ways to score 7 in total.

01:14 8 starts decreasing because 2 plus 6, 6 plus 2, 3 plus 5, 5 plus 3, 4 and 4, 9, 6 and 6, 6 and 5, 6 and 5, 6 and 5, 6, 5 and 5, 6, 6 and 5 and 5, 10, 6, 6, 5 and 5, 6, 5, 5, 6.

01:39 5, 5, 11, 6 and 5, 5 and 6.

01:46 So in total we have here 36 possible outcomes.

01:50 6 on the first die and 6 on the second, 6 times 6.

01:55 That's my sample space.

02:00 So we have here then 36 outcomes.

02:05 Make the numbers 2 to 12.

02:08 Now what i want in the first one, p.

02:15 Of event a and the sum is greater than six.

02:23 So, as i mean, it's from 36.

02:27 My outcomes here.

02:30 How many of those outcomes are above six? let's have a look...