- Suppose That You Have 7 Cards 3 Are Green And 4 Are Yellow The Cards Are Well Shuffled Suppose That You Randomly Draw 1 (34.24 KiB) Viewed 31 times
- Suppose That You Have 7 Cards 3 Are Green And 4 Are Yellow The Cards Are Well Shuffled Suppose That You Randomly Draw 2 (20.81 KiB) Viewed 31 times
Suppose that you have 7 cards. 3 are green and 4 are yellow. The cards are well shuffled. Suppose that you randomly draw two cards, one at a time, with replacement. • G₁ = first card is green • G₂ = second card is green . Ⓒ Part (a) Draw a tree diagram of the situation. (Enter your answers as fractions.) G Y 4/7 GG G 3/7 9/49 3/7 Y, 4/7 GY, 12/49 Part (b) Enter the probability as a fractic P(G, AND G₂) = 9/49 Part (c) Enter the probability as a fraction. P(at least one green) = 33/49 Ⓒ Part (d) Enter the probability as a fraction. P(Gz\G,)=| = 27/343 X 3/7 12/49 YG 4/7 16/49
Part (d) Enter the probability as a fraction. P(G, I G,) = |27/343 X Part (e) Are G₂ and G, independent events? Explain why or why not. O G₁ and G₂ are independent events because the probability of choosing a green card each time is the same. 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. Ⓒ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 not independent because they are the same color card.