Consider a standard deck of 52 playing cards. A card is randomly chosen from a deck of 52 cards, replaced, and a second card is chosen. 1. Would you say that the two draws are independent of each other i.e. are the outcomes on each of the two draws independent of each other? Why or Why Not? 2. Suppose that after the first draw, the card drawn is not replaced in the deck. Would you say that the two draws are independent of each other i.e. are the outcomes on each of the two draws independent of each other? Why or Why Not? 3. Consider the following three events as defined below: Event A: Drawing a Spade Event B: Drawing a King Event C: Drawing a Red Card a. Are events A and B Non-overlapping or Overlapping? Why or Why not? b. Are events A and C Non-overlapping or Overlapping? Why or Why not? Note: If you are like me, and not very familiar with what a deck of playing cards constitutes off, make sure you go through this link to understand it first.

Sally and Mike are playing frisbee at the beach. When Sally throws the frisbee the probability is 0.13 that it comes back to Sally, the probability is 0.7 that it goes to Mike, and the probability is 0.17 that the dog runs away with the frisbee. When Mike throws the frisbee there is a 0.62 probability that Sally gets it, a 0.27 probability that it comes back to Mike, and a 0.11 probability that the dog runs away with the frisbee. Treat this as a 3--state Markov Chain with the dog being an absorbing state. (a) If Mike has the frisbee, what is the expected value for the number of times the frisbee will be thrown before the dog gets the frisbee and runs away with it? (Give your answer correct to 2 decimal places.) times thrown (b) If Mike has the frisbee, what is the expected value for the number of times Mike will throw the frisbee before the dog gets it? (Give your answer correct to 2 decimal places.) times Mike throws

An experiment consists of rolling a fair die twice. Let A be the event that in the second roll the die lands 1, 2, or 5; B be the event that in the second roll the die lands 4, 5, or 6; and C be the event that the sum of the two outcomes from the two rolls is 9. Please choose the correct answer:

Need help with this Intro to probability and statistics homework problem.   Mutually exclusive events and independent events are often confusing when first learned. In your own words, give a brief explanation of the difference between the two and an example of each. The brief explanation is 70 points and the example is 15 points.

If events A and B are independent, then P(A U B) = 0. True or false?

What does it mean for two events to be mutually exclusive?

From an example in real life, give the probabilities of two events and the probability of both events occurring.  Based on these events, phrase a question about a conditional probability