Study of aggressiveness and birth order. Psychologists tend to believe that there is a relationship between aggressiveness and order of birth. To test this belief, a psychologist chose 500 elementary school students at random and administered each a test designed to measure the student’s aggressiveness. Each student was classified according to one of four categories. The percentages of students falling into the four categories are shown here.
Firstborn | Not Firstborn | |
Aggressive | 15% | 15% |
Not Aggressive | 25% | 45% |
a. If one student is chosen at random from the 500, what is the probability that the student is firstborn?
b. What is the probability that the student is aggressive?
c. What is the probability that the student is aggressive, given that the student was firstborn?
d. If we have
A: {The student chosen is aggressive.}
B: {The student chosen is firstborn.} are A and B independent? Explain.
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