Question

100 students were asked if they like chocolate, vanilla, or strawberry ice cream. The following data were collected: - 56 like chocolate, but 21 of these like only chocolate. - 39 like vanilla, but 11 of these like only vanilla. - 48 like strawberry, but 17 of these like only strawberry. - 13 do not like any of these flavors. - 18 like all three flavors. a) Introduce the corresponding events and create a Venn diagram for these data. b) Given that a student likes chocolate, what is the probability he also likes strawberry? c) Is liking chocolate independent of liking strawberry?

          100 students were asked if they like chocolate, vanilla, or
strawberry ice cream. The following data were collected:
- 56 like chocolate, but 21 of these like only chocolate.
- 39 like vanilla, but 11 of these like only vanilla.
- 48 like strawberry, but 17 of these like only strawberry. - 13 do
not like any of these flavors.
- 18 like all three flavors.
a) Introduce the corresponding events and create a Venn diagram
for these data.
b) Given that a student likes chocolate, what is the probability he
also likes strawberry?
c) Is liking chocolate independent of liking strawberry?

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Added by Richard P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Steven Clarke

06/13/2022

Step 1

- Let \( C \) be the event that a student likes chocolate. - Let \( V \) be the event that a student likes vanilla. - Let \( S \) be the event that a student likes strawberry. Show more…

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100 students were asked if they like chocolate, vanilla, or strawberry ice cream. The following data were collected: - 56 like chocolate, but 21 of these like only chocolate. - 39 like vanilla, but 11 of these like only vanilla. - 48 like strawberry, but 17 of these like only strawberry. - 13 do not like any of these flavors. - 18 like all three flavors. a) Introduce the corresponding events and create a Venn diagram for these data. b) Given that a student likes chocolate, what is the probability he also likes strawberry? c) Is liking chocolate independent of liking strawberry?

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Transcript

00:02 Okay then, we have here 100 students, that's you, 100, the entire venn diagram.

00:08 And we have three flavors, chocolate c, another v, and s.

00:15 Now, we are told that 56 like chocolate, so 56 will go here in brackets.

00:25 That number is this plus this, plus this, plus this, that's 56.

00:32 And of those, 21 like only chocolate.

00:37 So 21 will go here.

00:40 That area is only chocolate.

00:44 Then 39 like vanilla.

00:47 So 39 goes here in brackets.

00:51 Again, this, this and this together make 39.

00:56 11 of those like only vanilla.

01:00 So 11 will go here.

01:03 And strawberry is 48.

01:06 So again, put it in brackets.

01:09 48, this and this and this make 48.

01:15 And 17 like only strawberry.

01:19 17 goes here.

01:22 Then 13 don't like any of the flavors.

01:25 So that means 13 goes outside.

01:31 And 18 like all three flavors.

01:34 So 18 goes here in the middle.

01:41 Okay, we're missing three areas.

01:43 I would call them x, y, and z.

01:50 I want to find x, y, and z somehow...

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