As an effort to reduce food waste, Yue has been buying "surprise bags" of baked goods from the local bakery that are sold at a great discount price. Yue, having taken MDM4U before, has calculated that the probability of a new "surprise bag" customer getting a bag containing a doughnut (their favorite) is 45%. The probability that the next bag they buy contains a doughnut when the previous bag contained one is 25%. The probability that the next bag they buy contains a doughnut when the previous bag did not contain one is 80%. Calculate the probability that a new "surprise bag" customer will get exactly 2 doughnuts from purchasing 3 bags (1 bag per week). Include a complete tree diagram in your answer for full marks