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Many psychologists believe that birth order and personality are related. To study this hypothesis, 400 elementary school children were randomly selected and then given a test to measure confidence. On the results of this test each of the students was classified as being either confident or not confident. The numbers falling into each of the possible categories are:
Firstborn
Not firstborn
Confident
62
60
Not confident
105
173
That is, for instance, out of 167 students who were firstborn children, a total of 62 were rated as being confident. Suppose that a student is randomly chosen from this group.
(a) What is the probability that the student is a firstborn?
(b) What is the probability that the student is rated confident?
(c) What is the conditional probability that the student is rated confident given that the student is a firstborn?
(d) What is the conditional probability that the student is rated confident given that the student is not a firstborn?
(e) What is the conditional probability that the student is a firstborn given that the student is confident?
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