a-d 2. An urn contains 4 balls numbered 1,2,3,4, respectively. Two balls are drawn without replacement....
An urn contains 5 balls numbered 1 to 5. Two balls are drawn replacement Let X be the sum of the two numbers drawn. (a). What are the possible values of X? (b). if let X be the subtraction of the two numbers drawn.What are the possible values of X? (c). if let X be the product of the two numbers drawn.What are the possible values of X? (d). if let X be the Quotient of the two numbers drawn.What...
An urn contains 8 balls numbered 1-8 and a ball is randomly drawn from the urn. Let A = “Ball number 2, 4 or 6 is chosen” and let B = “Ball number 3,4,5,6 or 7 is chosen”. Calculate the following probabilities: a)P(A) b) P(A') c) P(A∪B) d) P(A|B)
2. An urn contains two green balls and three red balls. Suppose two balls will be drawn at random one after another and without replacement (i.e., the first ball is not returned to the urn before the second one is drawn). (a) Find the probabilities of the events A-I A green ball appears in the irst draw (Note, in event B, the first draw is supposed unknown, for example, after the first draw,you do not look at what color the...
1.3-9. An urn contains four balls numbered 1 through 4 The balls are selected one at a time without replacement. A match occurs if the ball numbered m is the mth ball selected. Let the event A, denote a match on the ith draw i 1,2, 3, 4. 3! (a) Show that P(A)for each i 4! 2! (b) Show that P(A, nA,) =-, i 1! (d) Show that the probability of at least one match is (e) Extend this exercise...
Two balls are drawn, without replacement, from a bag containing 13 red balls numbered 1−13 and 4 white balls numbered 14−17. (Enter your probabilities as fractions.) (a) What is the probability that the second ball is red, given that the first ball is white? (b) What is the probability that both balls are even-numbered? (c) What is the probability that the first ball is red and even-numbered and the second ball is even-numbered?
1.3-9. An urn contains four balls numbered 1 through 4. The balls are selected one at a time without replacement. A match occurs if the ball numbered m is the mth ball selected. Let the event Ai denote a match on the ith draw, i = 1, 2, 3, 4. (a) Show that PIA)for each i. 3! 4 (b) Show that P(AMA) =-, i 치. 4!
Exercise 2.19. We have an urn with balls labeled 1,..., 7. Two balls are drawn. Let X1 be the number of the first ball drawn and X2 the number of the second ball drawn. By counting favorable outcomes, compute the probabilities P(X 1 = 4), P(X2 = 5), and P(X1 = 4,X 2 = 5) in cases (a) and (b) below. (a) The balls are drawn with replacement. (b) The balls are drawn without replacement. (c) Does the answer to...
Question 3. (exercise 3.11-13 in textbook) An urn contains r red balls and b blue balls. A ball is chosen at random from the urn, its color is noted, and it is returned together with d more balls of the same color. This is repeated indefinitely. What is the probability that (a) The second ball drawn is blue? (b) The first ball drawn is blue given that the second ball drawn is blue? (c) Let Bn denote the event that...
Question 3. (exercise 3.11-13 in textbook) An urn contains r red balls and b blue balls. A ball is chosen at random from the urn, its color is noted, and it is returned together with d more balls of the same color. This is repeated indefinitely. What is the probability that (a) The second ball drawn is blue? (b) The first ball drawn is blue given that the second ball drawn is blue? (c) Let Bn denote the event that...
an urn contains n red and n blue balls. Balls are drawn at random (without replacement) in stages until one color is depleted. The number of draws until this event happens is called waiting time. what is the distribution of this waiting time?