Question

State whether or not the situation in each case is a probabilistic situation, and tell why. If it is not a probabilistic situation, reformulate the situation so that it is a probabilistic one.

a. the probability that the U.S. secretary of state is a woman.

b. the probability that a person will be able to read newspapers more intelligently after completing this course.

c. the probability that the soon-to-be-born baby of a pregnant Mrs. Johnson with two sons will be a girl

d. the probability that a woman's planned third child will be a girl, given the information that her first two children are boys.

e. the probability that it will snow tomorrow in this city

f. the probability that Joe ate pizza yesterday

Answer 1

A probabilistic situation is a situation that has multiple outcomes, each of which has a non-zero probability of occuring.

a.) YES. The probability that the U.S. secretary us a woman is a probabilitic situation. This is because there are multiple outcomes to this particular situation. Generally speaking out of the two possible outcomes i.e. the gender of the US secretary can be either male or female, both having a non-zero probability of occuring.

b.)YES. This is also a probabilistic situation. Either the person would be able to read newspapers more intelligently after completing the particular course that is being talked about, OR he would not be able to read more intelligently OR there would be no difference. A variety of factors would influence the different outcomes, all of which are probable.

c.)NO. This is not a probabilistic situation. Since the baby is soon to be born, nature has already decided her gender which is not influenced now by the conditional information that she had two sons. Rephrased as "the proabability that the soon-to-be baby of Mrs. Johnson will be a girl" to become a proababilistic situation.

d.)YES. The probability that a woman's planned third child will be a girl, given the information that her first two children are boys. Apriori information about the gender of the already conceived children can show some level of correleation to the future child, which makes this a probabilistic situation.

e.) YES. Same logic as before. Weather patterns can change, and there is a chance it will snow tomorrow in the city assuming it has snowed before.

f.)NO. This is not a probabilistic situation. This event has already occured in the past and it is certain. This statement cannot be rephrased into a probabilistic situation.