#5: Probability and binomial variables 1) Define the term \"binomial variable\". Provide 3 example of binomial variables. 2) A student has received the following homework grades after 6 homeworks have been assigned. [52 90 61 33 24 80]. Is this variable binomial? If not, convert it to a binomial variable, and describe the method you used to convert it. Are there other ways you could have converted this variable to binomial? 3) After removing all the clubs from a deck of cards, you are left with a 39 card deck with Hearts, Diamonds, and Spades. Answer the following questions, assuming that after every draw of a card, that card is returned to this deck and reshuffled. What is the probability of: a) Drawing a red card? b) Drawing a heart or a red card? c) Drawing a jack or a red card? d) Drawing 4 red cards in a row? (WITH REPLACEMENT between each draw) 4) If a Student is guessing randomly on a true false quiz with 17 questions: a) What is the probability of getting 4 correct? b) What is the probability of getting 4 incorrect? c) What is the probability of getting AT LEAST 3 correct? d) What is the probability of getting MORE THAN 3 correct? e) What is this students probability of passing the test? (>%65) 5) If a student is guessing randomly on a multiple choice test with 4 possible responses per question, and 16 questions: a) What is the probability of getting 3 correct? b) What is the probability of getting 3 incorrect? c) What is the probability of getting AT LEAST 3 correct? d) What is the probability of getting MORE THAN 3 correct? e) What is the probability of getting 7 correct? f) What is the probability of getting AT LEAST 7 correct? g) What is this students probability of passing the test? (>%65) 6) Multiple choice: Answer each sub-question by stating whether the term indicated would increase, decrease, stay the same, or not enough info to say. (Note: \"increase\" and \"decrease\" refer to the absolute value.) a) In the binomial distribution, as N decreases, what happens to the value of the most likely outcome when P = .50? b) For any N, as P increases from .10 to .50, what happens to the value of the most likely outcome? c) For any N, as P increases from .50 to .90, what happens to the value of the most likely outcome? d) When P = .5, what happens to the probability of the most likely individual outcome, as N increases? e) When P = .8, what happens to the probability of the most likely individual outcome, as N increases? f) In the binomial distribution, what happens to the value of the most likely individual outcome as N increases and, at the same time, P increases? g) When P = .5, what happens to the individual probabilities of the very most extreme outcomes (that is, the very highest and lowest possible outcomes) as N increases? 7) a) We have a coin and each toss can have only two outcomes, Head or Tail. Suppose we toss the coin 10 times. If we want all of the ten outcomes to be head then what will be the probability for this? a) We have a coin and each toss can have only two outcomes, Head or Tail. Suppose we toss the coin 10 times. If we want the first 7 tosses to come up head and the last 3 to come up tail, then what will be the probability for this