By Kenneth Baclawski

FOREWORD PREFACE units, occasions, and likelihood The Algebra of units The Bernoulli pattern area The Algebra of Multisets the concept that of likelihood houses of chance Measures self sustaining occasions The Bernoulli technique The R Language Finite techniques the elemental types Counting ideas Computing Factorials the second one Rule of Counting Computing chances Discrete Random Variables The Bernoulli strategy: Tossing aRead more...

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16. To do this exercise one must assume that the player’s times at bat are independent. Is this a reasonable assumption? 19 Three pigeons have been trained to peck at one of two buttons in response to a visual stimulus and do so correctly with probability p. Three pigeons are given the same stimulus. , at least two) peck at the correct stimulus? Suppose that one of the pigeons sustains an injury and subsequently pecks at one or the other button with equal probability. Which is more likely to be the correct response, the button pecked by one of the normal pigeons or the button pecked by a majority of the three pigeons?

11 It is said that the Earl of Yarborough used to bet 1000 to 1 against being dealt a hand of 13 cards containing no card higher than 9 in the whist or bridge order. Did he have a good bet? In bridge the cards are ranked in each suit from 2 (the lowest) through 10, followed by the Jack, Queen, King and Ace in this order. 12 May the best team win! 55. What is the probability that the better team will win the World Series? Do this as follows. Treat the games as tosses of a biased coin. Express the event “the better team wins” in terms of elementary Bernoulli events, and then compute the probability.

17 A student applies for two national scholarships. The probability that he is awarded the first is 1/2, while the probability for the second is only 1/4. But the probability that he gets both is 1/6. Are the events that he gets the two scholarships independent of one another? Discuss what this means. 280 batting average. What is the probability that he is successful the next three times at bat? 16. To do this exercise one must assume that the player’s times at bat are independent. Is this a reasonable assumption?