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Exercise 1 An urn contains twenty identical balls numbered from 1 to 20. Alice and Bob play the following game. Alice randomly draws a ball, writes down its number and puts it back in the urn. Bob randomly draws a ball from the urn, writes down the number and leaves the ball outside the urn. Bob wins if the absolute value of the difference of the two numbers is less than or equal to 3. What is the probability that Bob wins ?

          Exercise 1
An urn contains twenty identical balls numbered from 1 to 20. Alice and Bob play the following game. Alice randomly draws a ball, writes down its number and puts it back in the urn. Bob randomly draws a ball from the urn, writes down the number and leaves the ball outside the urn. Bob wins if the absolute value of the difference of the two numbers is less than or equal to 3. What is the probability that Bob wins ?

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Exercise 1
An urn contains twenty identical balls numbered from 1 to 20. Alice and Bob play the following game. Alice randomly draws a ball, writes down its number and puts it back in the urn. Bob randomly draws a ball from the urn, writes down the number and leaves the ball outside the urn. Bob wins if the absolute value of the difference of the two numbers is less than or equal to 3. What is the probability that Bob wins ?

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Steven Clarke

02/07/2022

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Since there are 20 balls in the urn, Bob has 20 choices. Show more…

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Exercise 1 An urn contains twenty identical balls numbered from 1 to 20. Alice and Bob play the following game. Alice randomly draws a ball, writes down its number and puts it back in the urn. Bob randomly draws a ball from the urn, writes down the number and leaves the ball outside the urn. Bob wins if the absolute value of the difference of the two numbers is less than or equal to 3 . What is the probability that Bob wins? Exercise 1 An urn contains twenty identical balls numbered from 1 to 20. Alice and Bob play the following game. Alice randomly draws a ball, writes down its number and puts it back in the urn. Bob randomly draws a ball from the urn, writes down the number and leaves the ball outside the urn. Bob wins if the absolute value of the difference of the two numbers is less than or equal to 3. What is the probability that Bob wins ?

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Transcript

00:01 Okay, we have two urns here.

00:03 One contains balls with numbers 1, 2, 3, 3.

00:07 That's a, and b contains balls 3 through 10.

00:11 First thing we do, we pick one of the two urns.

00:15 There's a one -half chance.

00:16 We pick a and a one -half chance.

00:19 We pick b.

00:20 And part a says, i want to work out the chance that the ball chosen is numbered 1.

00:27 Well, that only occurs with earn a.

00:31 So to get a ball number one will be one chance out of three.

00:40 Three balls, only one is labelled one.

00:44 So my answer then will be one half times one third, which is one out of six.

00:53 So part a then, the answer is one sixth.

00:57 Two things must happen.

00:58 You must choose urn a and you must pick the one.

01:03 So here then question a.

01:07 Now part b, what chance is there? the ball is numbered three.

01:11 In green here, to get three from earn a is also a one -third chance.

01:21 There are three balls.

01:22 Only one is label three.

01:25 So this way then will be one -half times one -third as well, which is also, of course, one -sixth...

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