It is reported that 85% of Asian, 78% of white, 70% of Hispanic, and 38% of black children have two parents at home. Suppose there are 500 students in a representative school, of which 280 are white, 50 are Asian, 100 are Hispanic, and 70 are black. 

a. Are the events “Asian” and “black” mutually exclusive and exhaustive? Explain. 

b. What is the probability that a child is not white? 

c. What is the probability that a child is white and has both parents at home? 

d. What is the probability that a child is Asian and does not have both parents at home?