Question

Exercise 6. This problem describes an experiment in which conditional probabilities are used to compute "proper" probability. The experiment starts with two urns, Urn #1 contains 5 white marbles and 2 black marbles. Urn #2 contains 7 white marbles and 3 black marbles. One marble from each urn is drawn at random. (For each urn, the chance of each marble being drawn is the same.) Let T be the event that the two marbles are the same color. Let W be the event that the marble from Urn #1 is white. (A) Find P(W). (B) Find P(T | W) (C) Find P(Tnw). (D) Find P(T | W"). (E) Find P(T). Exercise 7. die are rolled. Let Y be the number of 6's rolled. Define a random variable as follows: Twenty-one fair six-sided (A) Find n and p such that Y is equivalent to the binomial variable Bin(n,p). (B) What is the probability that R 4? Give you answer to four places beyond the decimal point. (C) What is E(Y)? (D) Estimate the standard deviation of Y to the nearest hundredth.
ASAP

Answer 1

As per Chegg policy, when there are more than 1 distinct questions, we are expected to solve the first question. Solving Exercise 6 6) Givern White Black Total 2 Urn 1 Urn 2 Total w : event that marble from Urn #1 is white T: event that the two marbles are same color 10 17 12 5 A) P(W) P(marble from Urn 1 is white) P(W) 5/7 B) P(TI W) P(two marbles are same color | marble from Urn 1 is white) - P(marble from urn 2 is white | marble from urn 1 is white) -P(T AND W) / P(W) -P(both marbles are white) P(marble from urn 1 is white) -P(marble from urn 1 is white) P(marble from urn 2 is white) P(marble from urn 1 is white) (... since drawing marble from each urn is an independent event) -P(marble from urn 2 is white) PIT I W)-7/10 C) P(T n W) P(two marbles are same color AND marble from Urn 1 is white) -P(marble from urn 2 is white AND marble from urn 1 is white) -P(marble from urn 2 is white) P(marble from urn 1 is white) (... since drawing marble from each urn is an independent event) d) W-event that marble from Urn 1 is not white P(T W) P(two marbles are same color | marble from Urn 1 is black) = P(marble from urn 2 is black 1 marble from urn 1 is black) P(T AND W) P(W) - P(both marbles are black) P(marble from urn 1 is black) -P(marble from urn 1 is black)*P(marble from urn 2 is black) / P(marble from urn 1 is black) (... since drawing marble from each urn is an independent event) -P(marble from urn 2 is black) 3/10 P(T I W') 3/10 e) P(T) P(two marbles are same color) -P(both marbles are white) OR P(both marbles are black) 5/77/102/7 *3/10 - 1/2 3/35 41/70 P(T) - 41/70