00:01
In this problem, we have been given information about how many families have a dog and how many of them have a cat in a certain community, and we need to compute certain probabilities based on this.
00:11
So, first of all, let us consider d to be the event that a family owns a dog, and c to be the event that a family owns a cat.
00:18
Now, 36 % of families have a dog, so p of d will be 36%, that is 36 over 100 or 0 .36.
00:27
And it is said that 30 % have a cat, so the probability of c will be 30%, which is 30 over 100, or 0 .30.
00:35
And it is said that of those families with a dog, 22 % also have a cat.
00:40
That means that the probability of having a cat, given that a family has a dog, will be 22%, which is 22 over 100, or 0 .22.
00:49
Now, first of all, we have been asked to find the probability that a family has both a dog and a cat, so we want to find the probability of d and c.
00:58
Now we can find this using the multiplication rule of probability, and using that, this will be equal to p of d times p of c given d...