A group of 115 people were randomly selected and asked to...

A group of 115 people were randomly selected and asked to state their preferences for ice cream flavors: S-Strawberry, C - Chocolate, V- Vanilla. The data collected is as follows: 42 like Vanilla 55 like Strawberry 48 like Chocolate 15 like Strawberry and Chocolate 26 like Vanilla and Strawberry 17 like Vanilla and Chocolate 8 like all three flavors Draw a Venn diagram for the data given and answer the following questions: (a) How many persons prefer chocolate or vanilla but not strawberry flavored ice cream? (b) How many persons like at most two of the choices? (c) How many persons only one flavor? (d) How many persons do not like any of three flavors?

Transcript

00:01 A group of 115 people were randomly selected and asked to state their preference for ice cream flavors.

00:07 We have strawberry, chocolate, and vanilla.

00:11 The data collected is as follows.

00:13 42 -like vanilla, 55 -like strawberry, 48 -like chocolate, 15 -like strawberry and chocolate, 26 -like vanilla and strawberry, and 17 -like vanilla and chocolate.

00:25 Eight like all three flavors.

00:27 So if we draw a venn diagram and we'll have strawberry, chocolate, and vanilla, we're going to have eight people that like all three flavors.

00:41 So we're going to put that right in the middle where the intersection of all three circles.

00:47 Then the people that like two flavors, we have strawberry and chocolate.

00:55 There's 15 people, but we've already included eight of those in the liking of the three.

01:00 Three flavors.

01:02 So there's going to be a seven that will be in the intersection of strawberry and chocolate.

01:08 Vanilla and strawberry will be, they said that there was 26 of them.

01:14 So again, we have to subtract the eighth adding also like chocolate.

01:19 So our intersection of strawberry and vanilla will be 18.

01:23 Vanilla and chocolate, they said we're 17 people.

01:27 Again, subtract the eighth that also like the other two flavors.

01:31 And we come up with no.

01:32 Nine that like vanilla and chocolate.

01:36 So that gives us the people that only like one flavor.

01:41 So the ones that like vanilla only, we're going to start with the 42.

01:46 We're going to subtract out the eight that like all three.

01:49 Then we'll take the 26 that liked the vanilla and strawberry and subtract out the eight that already included strawberry and and we'll also going to subtract out the 17 that liked vanilla and chocolate, but we have to subtract the eight out from that.

02:09 So the ones that like vanilla only will be seven...

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