![]() Suppose that N independent trials of this experiment are The outcomes of an experiment are 0, 1, and 2, and they occur with probabilities p0, p1, and p2 , What are their probabilities of winning?ħ. (c) Repeat if there are only two players Alice and Bob, but now under the assumption that whenĪlice rolls the dice, she wins with probability p1, while when Bob rolls the dice, he wins To player Pk, and so on until one of them wins. ![]() (b) Repeat if there are k players in this game, passing the dice from player P1, to player P2. What are their respective probabilities of winning? They continue to pass the dice back and forth until one of them Alice rolls the dice first, and if she fails to win, she passes the dice to Bob, who thenĪttempts to win on his roll. (a) The probability of winning on a single roll of dice is p. Independent, and events A and C are independent.Ħ. That is, events A and B are independent, events B and C are Show, however, that events A, B,Īnd C are pairwise independent. Show that A, B, and C are not independent. Let B be the event that the second toss lands heads, and let C be the event that both land on Let A be the event that the first toss lands heads, Consider two independent tosses of a fair coin. Determine whether the following statement is true or false and prove your answer: If events AĪnd B are independent, then they are conditionally independent given any event E.ĥ. The conditional probability that component 1 works given that the system is functioning.Ĥ. ![]() System consisting of n independent components, each of which works with probability 0.5. A parallel system functions whenever at least one of its components works. Were 0.8, could A and B be independent? Could they be disjoint?ģ. What is P( A ∪ B) if A and BĪre independent? What is P( A ∪ B) if A and B are disjoint? If P( A) were 0.6, and P( B) (b) Suppose that events A and B have P( A) = 0.3, P( B) = 0.4. ![]() Show that the probability of this event is (a) Suppose that an event A is independent of itself. Would you rather be player A or player B? Explain your answer and justify it by computing theĢ. Assuming that each spinner is equally likely to land in any one of its three regions, Then player B chooses one of the two remaining spinners.īoth players then spin their spinner and the one that lands on the higher number is declared Player A chooses one of the three spinners below, and Department of Electrical and Computer Engineeringġ. ![]()
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