You roll two six sided fair dice a let a be the event that...

'You roll two six-sided fair dice a. Let A be the event that the first die is odd and the second is a 4, 5, or 6 P(A) Round your answer to four decimal places. b. Let B be the event that the sum of the two dice is 10_ P(B) Round your answer to four decimal places. C. Are A and B mutually exclusive events? No, they are not Mutually Exclusive Yes, they are Mutually Exclusive Are A and B independent events? They are not Independent events They are Independent events'

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Transcript

00:01 For this exercise, we consider rolling a six -sided die twice, and we have defined an event a as the first die being odd, and the second being a four, a five, or a six.

00:15 And for part a, we are asked to find the probability of event a.

00:20 And here we can use the classic approach to probability, which says that for a sample space that has equally likely outcomes, so in this case, the sample space is the 36 possible dice rolls.

00:34 Then the probability of a given event is equal to the number of outcomes resulting in that event divided by the total possible number of outcomes in the sample space.

00:46 So this is the number of outcomes that satisfy event a, divided by the number of outcomes in the sample space.

00:56 So let's identify all dice rolls that satisfy event a.

01:01 The first die has to be odd, and the second is 4 or 5 or 6.

01:05 So it's these outcomes highlighted in yellow.

01:12 And there is a total of nine of them.

01:15 The total number of possible dice rolls when rolling a die twice is 36.

01:22 And so this comes out to one quarter.

01:27 And then for b, we want to find the probability that the sum is 10.

01:39 There are three outcomes for which the sum is 10.

01:43 These three here.

01:53 So we have 3 over 36.

02:01 This comes out to 0 .0833 approximately...