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Problem 5 There are 26 children at a birthday party. First, every child is asked if they would like a red balloon. Each child says yes or no. Next, every child is asked if they would like a yellow balloon. Each child says yes or no. So at the end of this process, there will be some children with 2 balloons (one red and one yellow), some children with a red balloon but not a yellow balloon, some children with a yellow balloon but not a red balloon, and some children with zero balloons. Given information: 14 children have a red balloon. (Each of these 14 children may or may not also have a yellow balloon.) 5 children have zero balloons. 11 children have two balloons. (These children have one red balloon and one yellow balloon.) 5a If a child at the party is selected at random, what is the probability they have exactly one balloon? 5b If a child at the party is selected at random, what is the probability they have a red balloon OR they don't have a yellow balloon? 5c If a child at the party is selected at random, what is the probability they have a yellow balloon given they have a red balloon?

          Problem 5
There are 26 children at a birthday party. First, every child is asked if they would
like a red balloon. Each child says yes or no. Next, every child is asked if they
would like a yellow balloon. Each child says yes or no. So at the end of this
process, there will be some children with 2 balloons (one red and one yellow),
some children with a red balloon but not a yellow balloon, some children with a
yellow balloon but not a red balloon, and some children with zero balloons.
Given information:
14 children have a red balloon. (Each of these 14 children may or may not also
have a yellow balloon.)
5 children have zero balloons.
11 children have two balloons. (These children have one red balloon and one
yellow balloon.)
5a
If a child at the party is selected at random, what is the probability they have
exactly one balloon?
5b
If a child at the party is selected at random, what is the probability they have a
red balloon OR they don't have a yellow balloon?
5c
If a child at the party is selected at random, what is the probability they have a
yellow balloon given they have a red balloon?

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Problem 5
There are 26 children at a birthday party. First, every child is asked if they would
like a red balloon. Each child says yes or no. Next, every child is asked if they
would like a yellow balloon. Each child says yes or no. So at the end of this
process, there will be some children with 2 balloons (one red and one yellow),
some children with a red balloon but not a yellow balloon, some children with a
yellow balloon but not a red balloon, and some children with zero balloons.
Given information:
14 children have a red balloon. (Each of these 14 children may or may not also
have a yellow balloon.)
5 children have zero balloons.
11 children have two balloons. (These children have one red balloon and one
yellow balloon.)
5a
If a child at the party is selected at random, what is the probability they have
exactly one balloon?
5b
If a child at the party is selected at random, what is the probability they have a
red balloon OR they don't have a yellow balloon?
5c
If a child at the party is selected at random, what is the probability they have a
yellow balloon given they have a red balloon?

Added by Jason G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jessica Horn

02/26/2022

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Step 1: There are 26 children at the party. Show more…

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There are 26 children at a birthday party. First, every child is asked if they would like a red balloon. Each child says yes or no. Next, every child is asked if they would like a yellow balloon. Each child says yes or no. So at the end of this process, there will be some children with 2 balloons (one red and one yellow), some children with a red balloon but not a yellow balloon, some children with a yellow balloon but not a red balloon, and some children with zero balloons. Given information: 14 children have a red balloon. (Each of these 14 children may or may not also have a yellow balloon.) 5 children have zero balloons. 11 children have two balloons. (These children have one red balloon and one yellow balloon.) 5a If a child at the party is selected at random, what is the probability they have exactly one balloon? 5b If a child at the party is selected at random, what is the probability they have a red balloon OR they don't have a yellow balloon? 5c If a child at the party is selected at random, what is the probability they have a yellow balloon given they have a red balloon?

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Transcript

00:01 Okay, so the question asked to draw a venn diagram of the information.

00:05 So i'm going to start with my venn diagram.

00:14 That kind of looks kind of bad.

00:15 Let's see, rice.

00:18 Let's see if we can try again.

00:22 All right, so there's a probability.

00:27 So there's 19 total.

00:30 They're either red balloon, yellow balloon, or the overlap, or the outside, which is none.

00:38 It tells you that there are three kids.

00:42 With no balloons.

00:44 So they're on the outside.

00:45 There are five kids who have both.

00:49 I skipped the beginning because it said there were seven kids who have a red balloon.

00:55 But in that red balloon, it doesn't say they have only red balloons.

01:00 So you have to assume that it is red and they have red period, red or yellow.

01:08 So you would take this five that's in the overlap and subtract it to get two because this total is seven red.

01:19 Okay? so that leaves us of the 19, that accounts for 10 kids.

01:24 That leaves us with nine who got just yellow.

01:29 So from there you can answer your questions.

01:32 So what's the probability that a kid got one balloon? the probability of one balloon are the ones that are only red and only yellow.

01:46 Yellow.

01:47 So that would be 11 out of the 19 kids.

01:53 The next question was the probability of red or, which is also the union, not yellow.

02:08 So red or not yellow...

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