Did you know?
Did you know that if we have a certain Algebra 2 class of 21 students, with 6 students playing basketball and 10 students playing baseball, the probability that a student chosen randomly from the class plays both basketball and baseball can be found using the principle of inclusion-exclusion? This principle states that the probability of two events occurring together is equal to the sum of their individual probabilities minus the probability of their intersection. In this case, the probability of a student playing basketball is 6/21 and the probability of a student playing baseball is 10/21. Since there are 7 students who play neither sport, their probability would be 7/21. Using the principle of inclusion-exclusion, we can find the probability of a student playing both sports by subtracting the probability of playing neither sport from the sum of the probabilities of playing each individual sport. So, the probability that a student chosen randomly from the class plays both basketball and baseball would be (6/21) + (10/21) - (7/21) = 9/21 = 3/7.
