1) Let P(A)=0.24,P(B)=0.51 and P(A or B)=0.75. Are events A and B mutually exclusive? Why or why not? 2) Suppose A and B are events such that P(A)=0.46,P(B)=0.5 and P(A or B)=0.77. Calculate the following: a) P(A and B)= b) P(AB)= c) P(BA)= d) P(AC)= e) P(BC)= f) Are A and B mutually exclusive? Why or why not? g) Are A and B independent? Why or why not? 3) One card is selected from an ordinary deck of 52 cards. Find the conditional probabilities: (You can write answer as a fraction or decimal rounded to three decimal places.) a) A Jack or Queen given the card is red. b) A spade given the card is red. c) A Jack given the card is a picture card. d) A 2 or 3 given the card is not a picture card. e) An King given the card is not a 2, 4, 6 or 8 . 4) A box contains 13 balls: 8 blue, 4 red, and 1 green. Two balls are selected without replacement. Find: a) P( both balls are blue )= b) P (both balls are green )= c) P( both balls are red )= d) P (the first ball is blue and the second is green) = e) P( the first ball is red and the second is blue) = f) P (one is red and one is green in any order) = 5) Let X represent the number of people in a household in the United States in 2021. a) Find P(3). b) Find P( More than 4). c) Find the probability that a randomly picked household contains 6 people. d) Find the probability that a randomly picked household has less than 3 people. e) Compute the mean x. f) Compute the standard deviation x. 6) An investor is considering a $25,000 investment in a start-up company. She estimates that she has a probability of 0.45 of a $60,000 loss, probability of 0.25 of a $40,000 profit, probability of 0.20 of a $15,000 profit, and probability 0.10 of breaking even (a profit of $0 ). a) Create a discrete probability distribution. b) What is the expected value of the investment? c) Would you advise the investor to make the investment? Explain why?.