please help with all parts. thank you!

Suppose that you have 8 cards. 5 are green and 3 are yellow. The cards are well shuffled. Suppose that you randomly draw two cards, one at a time, with replacement. - G1 = rst card is green - G2 = second card is green Draw a tree diagram of the situation. (Enter your answers as fractions.) Enter the probability as a fraction. Hemmer: El Part (0) Enter the probability as a fraction. P(at least one green) = C] E] Part (d) Enter the probability as a fraction. P(G2 | G1) = Are 62 and G1 independent events? Explain why or why not. 0 G1 and 62 are independent events because the probability of choosing a green card each time is the same. 0 G1 and 62 are independent events because choosing a green card and replacing it does not affect the chances of choosing a second green card. 0 G1 and 62 are not independent because they are the same color card. 0 G1 and 62 are not independent because after choosing the rst green card, the second green card has less chance of being picked. Submit Answer Suppose that you are offered the following "deal." You roll a die. If you roll a six, you win $10. If you roll a four or ve, you win $5. If you roll a one, two, or three, you pay $4- What are you ultimately interested in here (the value of the roll or the money you win)? 0 the number of times a six is rolled O the type of die 0 the number rolled O the amount of winnings In words, dene the Random Variable X. 0 the amount of numbers that can be rolled O the amount of money made by rolling a six 0 the probability of rolling a four 0 the amount of winnings List the values that X may take on. 0 $4. $5, $10 O1,2,3,4,5,6 0 $4. $5,$1o 0 4,5,6 E] Part (d) Construct a PDF. (Enter your answers for P(X = X) as fractions. Round your answers for x - P(X = x) to two decimal places.) X P(X=x) x-P(X=x) 6 l m5 ] 1,2,or3 I E] Part (e) Over the long run of playing this game, what are your expected average winnings per game? (Round your answer to two decimal places.) Based on numerical values, should you take the deal? 0 Yes, you should take the deal because the expected value is positive. 0 No, you should not take the deal because the expected value is negative