Math 150, Fall 2021 El Camino College G. Song 11: A box contains 6 red ball and 9 blue balls. A ball is chosen at random from the bag and is not replaced; then a second ball is chosen. Construct a tree diagram and then find the probability that the two balls are of the same color. 12: The school tennis league consists of 12 players. Daniel has a 30% chance of winning any game against a higher-ranked player, and a 75% chance of winning any game against a lower-ranked player. if Daniel is currently in the third place, find the probability that he wins his next game against a random opponent. (Hint: Construct a tree diagram).Math 150, Fall 2021 El Camino College G. Song Section 4.3: Complements and Conditional Probability, and Bayes' Theorem 9: Definitions and Important Facts: . Notation and formula for conditional probability: P(A|B) = P(B|A) = . Interpret the complements: 1. Let A = getting at least one head. Then the complement, A is 2. Let A = getting at most three heads when we flip a coin 4 times. Then the complement, A is 10: Consider the contingency table below: Part Time Full Time Total Female 80 40 Male 60 20 Total a: What is the probability that a randomly selected student is a part time female student? b: What is the probability that a randomly selected student is part time, given that she is a female? c: What is the probability that a randomly selected student is female, given that she is a part time student