According to the Census’s Population Survey, the percentage of children with two parents at home is the highest for Asians and lowest for blacks (USA TODAY, February 26, 2009). 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 “Asians” and “black” mutually exclusive and exhaustive? Explain.
b. What is the probability that a given 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?