Pick the sample space (S) and the event (E) for the probability of of picking a red marble out of a bag that has yellow, green, red, and blue marbles. (S) the marbles O (E) picking a red marble O (S) picking a red marble O (E) the marbles

Addition of Rule of Probabilities P(A Or B)  = P(A) +P(B) – P(A and B)  for mutually exclusive events the last part P(A and B) is zero, why?

Toss a fair die and two fair coins. (Hint: Use (a) to compute (b) and (c)) (a) Write down the sample space. (b) Find the probability of getting exactly two heads. (c) Find the probability that the number on the die is at most 2.

Classify the events as independent or not independent. Events A and B where P(A) = 0.6, P(B) = 0.9, and P(A and B) = 0.54 Select one: a.independent b.not independent

Suzan sees a bag of marbles; she grabs a handful at random. She has seen a bagcontaining 4 red marbles, 3 green ones, 2 white ones, and 1 purple one. She grabs 5of them. Find the probability of the following event, expressing it as a fraction in lowestterms.(a) She has all the red ones (b) She has at least one white (c) two red and one of each of the other colors (d). She does not have all the red ones

Bayes' Theorem: Suppose that E and F are two events from a sample space S such that p(E)0 and p(F) 0. Then: Question: P(FE)= P(EF)P(F) P(EF)P(F)+P(EF)P(F) We have two boxes. The first box contains two green balls and seven red balls. The second contains four green balls and three red balls. Bob selects one of the boxes at random. Then he selects a ball from that box at random. If he has a red ball, what is the probability that he selected a ball from the first box. Let E be the event that Bob has chosen a red ball and F be the event that Bob has chosen the first box. The questions is: To find P(FIE) by using Bayes' theorem.

K Suppose Emerson wins 41% of all checker games. (a) What is the probability that Emerson wins two checker games in a row? (b) What is the probability that Emerson wins three checker games in a row? (c) When events are independent, their complements are independent as well. Use this result to determine the probability that Emerson wins three checker games in a row, but does not win four in a row. (a) The probability that Emerson wins two checker games in a row is (Round to four decimal places as needed.) (...)