2(a). A couple has three children. Suppose we know the elder child is a girl. Determine...

 

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2(a). A couple has three children. Suppose we know the elder child is a girl. Determine an appropriate sample space. Also find the probability that there are two boys in the family? (b). Suppose a Statistics class with 20 student, where 70% of those are female. It is known that in a test, 5% of males and 15% of females got an A grade. If a student from this class are randomly selected and observed to have A grade, what is the probability that one is a male students? 3(a). Let you have six chips of the same size in your bag. The alphabet a, b and c are written on exactly one, two and three chips, respectively. The experiment is to select one chip at random and read the alphabet y on the chip. Can you judge the probability mass function of the random variable y? Also, perform this experiment manually up to 500 times on your answer book sheet and compare these experimental probabilities and the theoretical probabilities with the help of histogram. 2(a). A couple has three children. Suppose we know the elder child is a girl. Determine an appropriate sample space. Also find the probability that there are two boys in the family? (b). Suppose a Statistics class with 20 student, where 70% of those are female. It is known that in a test, 5% of males and 15% of females got an A grade. If a student from this class are randomly selected and observed to have A grade, what is the probability that one is a male students? 3(a). Let you have six chips of the same size in your bag. The alphabet a, b and c are written on exactly one, two and three chips, respectively. The experiment is to select one chip at random and read the alphabet y on the chip. Can you judge the probability mass function of the random variable y? Also, perform this experiment manually up to 500 times on your answer book sheet and compare these experimental probabilities and the theoretical probabilities with the help of histogram.