In a survey poll of 500 students, 205 drive their own...

In a survey poll of 500 students, 205 drive their own vehicle, 112 ride their own motorcycles, and 197 students rely on other means of transportation. a) Find the probability that a student owns only a vehicle or a motorcycle. (Draw a Venn diagram) b) Find the probability that a student owns both a vehicle and a motorcycle. (Draw a Venn diagram) c) Are the two events mutually exclusive? Why or why not?

Transcript

00:01 Here we are given that in a survey 500 students are interviewed and we have that so the universal set has 500 students and there are students that that ride motorcycles and there are students that drive their own cars so for motorcycles we are going to call it m and for their own we're going to call it v.

00:36 Now, so here, let the students who have their own vehicle only, but don't cycle bx.

00:47 And the students who do both have a vehicle and have a motorcycle, let's call them y.

00:53 And the students who just have a motorcycle, let's call them z.

00:57 But then remember that there are students who rely on other means of transport.

01:02 And these are 197 so here we have one hundred and ninety seven now we know that the total number of students should add up to 500 so we can say 500 is equal to x plus y plus z plus 1097 so we'll call this equation one next we are told that five five five drive their own vehicle.

01:38 So in v we have 205 and 112 ride their own motorcycles.

01:46 So for m we have 112.

01:50 So here we have other the other equations as x plus y is equal to v which is 200, 205 and we'll call this equation 2 and y plus z is equal to 112, we'll call this equation 3.

02:15 Now, if we add, if we subtract equation 2 minus equation 3, we have the y subtracting out and we have x, x minus z.

02:38 X minus z.

02:43 Instead of subtracting these two, we call could actually because we observe that in the main equation we have y plus z and we actually have a y plus z here is equal to 112 so instead of solving this the the elimination way we could just take one hundred and twelf plug it in here and we will be left with just one unknown which is x so plugging into equation 1 we get 500 is equal to x plus now instead of y plus z we put 1112 plus 197 and we can see here that we can actually find the value of x x is equal to 500 minus 112 plus 197 and here we get the value of x of x and watch out for the brackets there the value of x is 191 now that we have the value of x we can plug this value into equation two to find the value of y so 191 plus y is equal to two hundred and five therefore our y will be 205 minus 191 and here we get 14 so y is 14 and our z will be equal to from equation 3, 101 minus y, which is 14, and we get our z as 98.

04:41 Now we have the value of x, y, and z.

04:48 So we can, i'm going to rub this off.

04:52 You can always go back to see how we got these values.

04:58 And i'm going to create another...

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