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- Suppose that you have 7 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards with replacement. Round your answers to four decimal places. G1 = the first card drawn is greenG2 = the second card drawn is green a. P(G1 and G2) = b. P(At least 1 green) = c. P(G2|G1) =The zebra plays a game in which in every turn she randomly chooses a letter from the set {A,B,C}, independently of other turns, and registers the outcome in a list. 1. Assume that the zebra plays exactly 4 turns, and let X denote the number of distinct outcomes she registers. 2. The first moment of X is 3. The probability that both A and B are registered at some point during the 4 turns she plays is 4. The second moment of X is 2. Now assume that the zebra plays until she registers every possible outcome at least once, that is, once she has registered at least one of each of the outcomes she stops. The expected number of turns she plays isSuppose E= "sum is 5" and F= "exactly one of the dice is even". Are E and F independent? Explain why or why not.
- A. A pair of dice is rolled. If X is the sum of pairs of numbers. 1. What is the P(X) which is divisible by 4? 2. What is P(X) which is divisible by 3?n 11 A coin is tossed and a die is rolled. The probability of getting a tail on the coin and an even number on the die is ed out of Select one: question O a. 1/3 O b. 0 O c. 1/4 O d. 1/2 Next pac Is pageT1.2 A person entering a university building is a student (S), faculty (F), or staff (W). We observe three successive persons entering the building. a) List all outcomes in the event A that exactly two are students. b) List all outcomes in the event B that the third person is a faculty
- In a random experiment if a coin is tossed three times or three coins are tossed one time, if random variable X is the number of appearances of Tails, the value of E(X), will be; Select one: O a. None O b. 3.5 O c. 2.5 O d. 1.5Roll a pair of fair six-sided dice and let X be 1 if the dice land showing the same number of spots, and 0 otherwise. For example, if both dice land 2, then X = 1, but if one lands 2 and the other lands 3, then X = 0. What is P(X = 1)? Explain your reasoning below.G is defined as this fair spinner landing on a multiple of 4. H is defined as the spinner landing on 11 or higher. What is P(G AND H)? Give your answer in decimal form.