If event A is independent of event B and A is independent of event C. Which of the following statements is true? a) P(A ∩ B) = P(A ∩ C) b) B and C are alien or disjoint c) B and C are independent d) None of the above.
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2. If
following statements is true?
a) P(A ∩ B) = P(A ∩ C)
b) B and C are alien or disjoint
c) B and C are independent
d) None of the above.
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- 5- The number of combinations of 5 elements that can be selected from 10 elements, is a) 250 b) 251 c) 252 d) 253 6- If the event A is included in the event B than: a) P(ASB) b) P(A2B) c) P(1-P(A)) d) P(1-P(B))If the student attends class on a certain Friday, then he is three times as likely to be next Friday as to attend. If the student is absent on a certain Friday, then he is four to attend class the next Friday as to be absent again. Assume that state 1 is Attends Class and that state 2 is Absent from Class.Which of the following expressions represents the number of distinguishable permutations of the letters of the word CONCLUSIONS? O 11!/(2!2!2!2!) 11!/8! O 11!/(2!2!2!) O 11!
- ”A is a subset of B. Therefore A is a subset of P(B).” This statement is incorrect as written. Assuming the first sentence is true, what is incorrect about the second sentence? State the second sentence correctly.Choose the right answer quickly pleaseA special plate number is made up of 2 letters of the vowel followed by 3 digit numbers. How many plate numbers are there if the letters and digits cannot be repeated in the same plate number? O 14,400 O 14,000 O 7,200 O 7,000 In how many ways can 7 persons be seated around a circular table? O 5040 O 2040 O 1040 O 720
- a) only II B) IV only NS) only I D) III and IV TO) only IIISuppose a card is drawn from a standard 52 cards deck. Spades, Diamonds, Clubs, Hearts Let A denote the event "the card drawn is black" and B denote the event "the card drawn is diamond". Are A and B independent? Are they mutually exclusive? O Not independent, not mutually exclusive. O Mutually exclusive and independent. O Independent but not mutually exclusive. O Mulually exclusive but not independent.4. A bag of fast-food sandwiches contains two hamburgers, four cheeseburgers, and three chicken burgers. If Wyatt ordered a cheeseburger and a chicken burger, what is the probability that a) the first sandwich selected will be one of his choices? b) neither of the first two sandwiches will be among Wyatt's choices? 5. Petra has mastered the proofs for six of ten theorems. Two of the theorems will appear as questions on the final examination. What is the probability that a) neither of the proofs on the examination will be among those Petra mastered? b) at least one of the mastered proofs will appear on the examination? 6. A pizza contains three toppings randomly selected from the following choices: pepperoni, mushrooms, green peppers, ham, bacon, and onions. Manuel enjoys all toppings, except bacon and onions. What is the likelihood that a pizza will contain a) no toppings that Manuel dislikes? b) exactly one topping that Manuel dislikes? c) at least one topping that Manuel dislikes? 7.…
- ASAPP!! Suppose there are three urns. Urn 1 contains two red balls and three black balls. Urn 2 contains one red ball and three black balls. Urn 3 contains four red balls and two black balls. A ball is drawn at random from Urn 1. If it is red, a second ball is drawn at random from Urn 2, but if it is black, the second ball is drawn at random from Urn 3. a) What is the probability of the second ball being drawn from Urn 3? b) What is the probability that the second ball is black, given that it is drawn from Urn 2? c) What is the probability that the second ball is black? (broad explanation)a) There are 6 balls in the bowl, of which 0 is white and the rest black. Person A has no knowledge of how to make balls the colors are determined, so according to his preconception all options (0,1,2,3,4,5,6) for 0 are equal likely. The person B picks up the ball from the bowl at random, returning it to the bowl and says the color is black. B repeats this one more time and says the color is black again. Person A does not know person B. Person A tries to figure out the number of white balls in the bowsl using Bayesian inference. Express by listing the values or, if desired, also by the formula i) the prior distribution of from the perspective of person A, ii) likelihood function the person A uses, iii) the person A' posterior distribution for 0. What is the most probable value of from the perspective of person A after making the observations? b) Continuation: The person C is listening the same experiment, without seeing the bowl either. Person C happens to know person B and knows that…
