00:01
Two fair six -sided dice number one of six are rolled at the same time and you can okay, enter reduced fractions only so what is the priority that the sum of the dice is more than six or or at least one dice rolled a four okay, what is the what is the number of options in which as first of what are the total number of options so the sample is space well definitely since there are are two dies so one dice has six options other dice has six options so 36 total options now the sum should be more than six okay if the first if the first dice has rolled one then the second dice must roll six so that because that is the only way in which one plus six is seven which is more than six right if that's five then the sum is six but they need more than six and the second die rolls two then the third dice then the the first dice rolls two then the second dice can have either five or can have six because this sum is seven and this sum is eight and both are allowed because they are more than six likewise we have three four three five three six likewise we have four three four four four five four six and i think you get an idea right so there's one option here two option here three option here four option here five option next and six options over the last one so 6 plus 4 is 10, 10 plus 5 is 15, 16, 17, 18, 19, and 21.
01:39
There are 21 such options.
01:42
Let me calculate it again.
01:44
6 plus 4 is 10, 15, 60, 17, 18, 19, 21.
01:47
There are 21 such options in which the sum is more than 6.
01:53
But we also, we can also include the numbers that has at least one dice rolled for.
02:00
So what are the possible options? let's say the first dice has rolled four.
02:07
So the other dice can roll, let's say, any number which is not four.
02:11
So one, two, three, five, six.
02:14
There are five options, right? so there are five such options.
02:19
Another option can be the second dice has rolled four and the first dies roll anything except four.
02:24
So again, five option.
02:25
And the third one is both the dice rolled four, which is one option.
02:29
But remember some of the options are already being counted for example 4 4 is already counted so we do not have to repeat it again for example we have the second number now as 4 so out of this 4 how many possible options are there it's 1 4 2 4 3 4 5 4 and 6 4 out of which 1 4 and 2 4 are not counted but this sum is already more than six so we have already counted so we can take these two numbers from here right so i'm going to add another two and likewise over here we had four one uh four two four three four four four four five and then we have four six so likewise we have not counted four one and four two but rest are already counted so again plus two so two plus two is four this will become 25 so the problem probability is going to be the favorable outcomes over the total outcomes.
03:35
So that's 25 over 36.
03:38
Let's talk about option b.
03:41
So option b talks about what's the probability that the sum is odd.
03:46
So it's i think a good idea if we can write the complete sample space because that's going to help us in all the three parts.
03:53
So it's one one, one two, one three, one four, one five and one six.
04:00
Then we have 2 -1 -2 -2 -2 -3 all right and then we have all right so here i have the complete sample space written which we are going to use again and again in all the parts so in part b this is the sample space which i'm going to make a copy on the other page just in case okay uh so let's go back and uh talk about part b so here we need the probability that the sum is odd or at least one dice has rolled three...