Reference no: EM132342726
A psychologist claims that people who are first-born in their families (i.e., the oldest child in their family) are more likely to succeed professionally in their adult life than those who are not first-born (i.e., individuals who have an older brother or sister). The psychologist suggests that the reason for this "fact" is that first-born individuals enjoy the undivided attention of their parents early on in life and this nurtures within them a drive to succeed. In support of his claim that first-borns are more likely to be high-achievers than those who are not first-born, he cites the fact that 60% of C.E.O.s of Fortune 500 companies are first-borns. Let us use our knowledge of probability to scrutinize this piece of evidence. The following table gives the probability distribution over the number of children in the families into which employees of Fortune 500 companies were born:
No.of children in family 1 2 3 4 Probability 0.3/0.4/0.21/0.08
Thus, the probability that a randomly chosen employee of a Fortune 500 company grew up in a household as the only child is 0.31, etc. (The probability of 5 or more children in a family is negligible.) Let CEO be the event that a randomly selected employee of a Fortune 500 company is a C.E.O. Let F be the event that a randomly selected employee of a Fortune 500 company is a first-born.
(a) What is the probability that a randomly selected C.E.O. of a Fortune 500 company is a first- born?
(b) What is the probability of F?
(c) What can you say about the relationship between events F and CEO?
(d) Does your analysis provide support for the psychologist's theory about first-borns? Explain briefly.