## A First Course in ProbabilityA First Course in Probability, Eighth Edition, features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus. |

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Results 1-3 of 75

Page 172

Suppose that we win $2 for each black ball selected and we lose $1 for each

white ball selected.

, and what are the probabilities associated with each value? 4.2. Two fair dice are

rolled. Let X equal the product of the 2 dice. Compute P{X = /'} for 1 = 1 36. 4.3.

Three dice are rolled. By assuming that each of the 63 =216 possible outcomes is

equally likely, find the probabilities attached to the possible values that X can

take on ...

Suppose that we win $2 for each black ball selected and we lose $1 for each

white ball selected.

**Let X denote**our winnings. What are the possible values of A', and what are the probabilities associated with each value? 4.2. Two fair dice are

rolled. Let X equal the product of the 2 dice. Compute P{X = /'} for 1 = 1 36. 4.3.

Three dice are rolled. By assuming that each of the 63 =216 possible outcomes is

equally likely, find the probabilities attached to the possible values that X can

take on ...

Page 174

Finally, another ball is chosen, and the team named on the ball (provided that it is

different from the previous two teams) receives the third draft pick. The remaining

draft picks 4 through 11 are then awarded to the 8 teams that did not "win the

lottery," in inverse order of their won-lost records. For instance, if the team with

the worst record did not receive any of the 3 lottery picks, then that team would

receive the fourth draft pick.

record.

Finally, another ball is chosen, and the team named on the ball (provided that it is

different from the previous two teams) receives the third draft pick. The remaining

draft picks 4 through 11 are then awarded to the 8 teams that did not "win the

lottery," in inverse order of their won-lost records. For instance, if the team with

the worst record did not receive any of the 3 lottery picks, then that team would

receive the fourth draft pick.

**Let X denote**the draft pick of the team with the worstrecord.

Page 182

Then try to express the events (A' > n) and {Y < r) in terms of the outcomes of this

sequence. 4.29. For a hypergeometric random variable, determine P{{

them are randomly selected without replacement.

number selected. (a) Find the probability mass function of Y. (b) Derive an

expression for E[Y] and then use Fermat's combinatorial identity (see Theoretical

Exercise 1 1 of ...

Then try to express the events (A' > n) and {Y < r) in terms of the outcomes of this

sequence. 4.29. For a hypergeometric random variable, determine P{{

**X**= k + \}/P{**X**= k} 4.30. Balls numbered 1 through N are in an urn. Suppose that n,n s A', ofthem are randomly selected without replacement.

**Let**Y**denote**the largestnumber selected. (a) Find the probability mass function of Y. (b) Derive an

expression for E[Y] and then use Fermat's combinatorial identity (see Theoretical

Exercise 1 1 of ...

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### Contents

Axioms of Probability | 22 |

Conditional Probability and Independence | 58 |

Random Variables | 117 |

Copyright | |

8 other sections not shown

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### Common terms and phrases

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