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Question

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%85 \% of Asian, 78%78 \% of white, 70%70 \% of Hispanic, and 38%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.

What is the probability that a child is not white?

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In this exercise, we need to find if the given events are mutually exclusive and exhaustive, the probability of a child not being white, the probability of a child being white and having both parents, and the probability of an Asian child who doesn't have both parents.

The exercise states that the children who have both parents at home are 85%85\% Asian (P(PA)=0.85P(P|A)=0.85), 78%78\% white (P(PW)=0.78P(P|W)=0.78), 70%70\% Hispanic (P(PH)=0.7P(P|H)=0.7), and 38%38\% black (P(PB)=0.38P(P|B)=0.38). There are 500500 students, 280280 of them are white, 5050 are Asian, 100100 are Hispanic, and 7070 of them are black.

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