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# An urn contains 17 balls marked LOSE and 3 balls marked ISBN: 9780321923271 41

## Solution for problem 8E Chapter 1.3

Probability and Statistical Inference | 9th Edition

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Problem 8E

PROBLEM 8E

An urn contains 17 balls marked LOSE and 3 balls marked WIN. You and an opponent take turns selecting a single ball at random from the urn without replacement.

The person who selects the third WIN ball wins the game. It does not matter who selected the first two WIN balls.

(a) If you draw first, find the probability that you win the game on your second draw.

(b) If you draw first, find the probability that your opponent wins the game on his second draw.

(c) If you draw first, what is the probability that you win? Hint: You could win on your second, third, fourth, . . . , or tenth draw, but not on your first.

(d) Would you prefer to draw first or second?Why?

Step-by-Step Solution:

Step 1 of 4 :

We have an urn contains 17 balls marked LOSE and 3 balls marked WIN. You and an opponent take turns selecting a single ball at random from the urn without replacement.

The person who selects the third WIN ball wins the game.It does not matter who selected the first two WIN balls.

a).

If you first, we need to find the probability that you win the game on your second draw.

Here we consider Y : you draw W first, O : opponent draws W first and

Y : you draw W second.

Then,

P(YOY) = P(W W W )

Where W is win.

P(YOY) = P(YOY) = Therefore the probability that you win the game on your second draw is .

Step 2 of 4 :

b).

If you first, we need to find the probability that your opponent wins the game on his second draw.

P(YOYO) = P(2 Win,1 Lose , 1 Win)

P(YOYO) = P(YOYO) = P(YOYO) = Therefore the probability that your opponent wins the game on his second draw is .

Step 3 of 4

Step 4 of 4

##### ISBN: 9780321923271

Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. The answer to “An urn contains 17 balls marked LOSE and 3 balls marked WIN. You and an opponent take turns selecting a single ball at random from the urn without replacement.The person who selects the third WIN ball wins the game. It does not matter who selected the first two WIN balls.(a) If you draw first, find the probability that you win the game on your second draw.(b) If you draw first, find the probability that your opponent wins the game on his second draw.(c) If you draw first, what is the probability that you win? Hint: You could win on your second, third, fourth, . . . , or tenth draw, but not on your first.(d) Would you prefer to draw first or second?Why?” is broken down into a number of easy to follow steps, and 123 words. This full solution covers the following key subjects: draw, Win, Probability, Game, balls. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. The full step-by-step solution to problem: 8E from chapter: 1.3 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. Since the solution to 8E from 1.3 chapter was answered, more than 914 students have viewed the full step-by-step answer.

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