Suppose that you have 9 cards. 4 are green and 5 are yellow. The cards are well shuffled. Suppose that you randomly draw two cards, one at a time, with replacement. Part (a) G₁ = first card is green = second card is green Draw a tree diagram of the situation. (Enter your answers as fractions.) G Y, 5/9 GG GY, 20/81 YG YY Part (b) Enter the probability as a fraction. P(G₁ AND G₂) = □ Part (c) Enter the probability as a fraction. P(at least one green) = Part (d) Enter the probability as a fraction. P(G₂ | G₁)= □ Part (e) Are G2 and G₁ independent events? Explain why or why not. OG₁ and G₂ are independent events because the probability of choosing a green card each time is the same. G₁ and G₂ are not independent because they are the same color card. O G₁ and G2 are not independent because after choosing the first green card, the second green card has less chance of being picked. O G₁ and G2 are independent events because choosing a green card and replacing it does not affect the chances of choosing a second green card.

Determine if the statement is true or false. If the statement is false, then correct it and make it true. If the probability that you will graduate is 0.63, then the probability that you will not graduate is -0.63.

Medicine Out of a group of 9 patients treated with a new drug, 4 suffered a relapse. Find the probability that 3 patients of this group, chosen at random, will remain disease-free.

Roulette American roulette is a game in which a wheel turns on a spindle and is divided into 38 pockets. Thirty-six of the pockets are numbered 1-36, of which half are red and half are black. Two of the pockets are green and are numbered 0 and 00 (see figure). The dealer spins the wheel and a small ball in opposite directions. As the ball slows to a stop, it has an equal probability of landing in any of the numbered pockets. (a) Find the probability of landing in the number 00 pocket. (b) Find the probability of landing in a red pocket. (c) Find the probability of landing in a green pocket or a black pocket. (d) Find the probability of landing in the number 14 pocket on two consecutive spins. (e) Find the probability of landing in a red pocket on three consecutive spins.