3 for the following questions consider the rolling of a die...

3. For the following questions, consider the rolling of a die twice sample space (put a box around your final answer): a. If a die is rolled twice, find the probability that the sum is 4. b. If a die is rolled twice, find the probability that the sum is 7 or the 1st roll is a 3. c. If a die is rolled twice, find the probability that the sum is 7 given that the 1st roll is a 4. d. If a die is rolled twice, find the probability that the sum is 6 given that the 2nd roll is a 3. e. When a die is rolled twice, are the event "sum is 10" and "1st roll is a 2" disjoint?

Transcript

00:01 All right, so your sample space is your possible outcome.

00:03 So if i roll a dice, let me just draw a little chart here.

00:07 If i roll two dice, the first one could land on a one, a two, a three, a four, or a five, or a six.

00:16 The second one can land a one, two, three, four, five, or six.

00:21 So i could have a one and a one, i could have a one and a two, a one in a three, a one and a four, a one and a five, or a one in a one and a one.

00:31 And a six i could have a two and a one a two and a two and a three a two and a four a two and a five and a two and a six i could have a three and a one four and a one a five and a one a five and a one a six and a one a three and a two a four and a two a five and a two or a six and a two a two a three and a three and a three and a four three and a five a three and a six and a two a two a five a three and a six um a four and a three a four and a four oh hold on i had to mess myself up because i wasn't going in order sorry all right so i could have a four and a three a five and a three a six and a three a four and a four and a five four and a six a five a four and a four a six a four i could have a five and a five or a five or a six and a five or i could have a five and a six or a six and a six so i have thirty six possible outcomes so what find the probability that the total sum is five so which one's total the total sum is five so here's a five here's five here's a five here's five so for part b the total sum is five is four out of 36.

02:18 Oh, write the event as well.

02:22 Okay.

02:23 So the probability of 5 equals 4 out of 36, which equals 1 out of 9.

02:35 So c says the probability of less than 5.

02:44 Well, how many are less than 5? 1, 2, 3, 4, 5, 6.

02:51 6 out of 36, which equals 1 .6.

02:58 Obtaining two even numbers.

03:01 So d is probability of both even.

03:08 So both even.

03:12 1, 2, 3, 4, 5, 6, 7, 8, 9...