1. determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial).for those that are not binomial, identify at least one requirement that is not satisfied.
a. the ysort method of gender selection, developed by the genetics & ivf institute, is designed to increase the likelihood that a baby will be a boy. when 291 couples use the ysort method and give birth to 291 babies, the genders of the babies are recorded
b. in an idaho potato company commission survey of 1000 adults, subjects are asked to select their favorite vegetables, and responses of potatoes, corn, broccoli, tomatoes, or "other" were recorded.
c. ten different us senators are randomly selected without replacement, and the numbers of terms they have served are recorded.
2. in the new york state win 4 lottery, you place a bet by selecting four digits. repetition is allowed, and winning requires that your sequence of four digits matches the four digits that are later drawn. assume that you place one bet with a sequence of four digits.
a. use the multiplication rule to find the probability that your first two digits match those drawn and your last two digits do not match those drawn. that is, find p(mmxx), where "m" denotes a match and "x" denotes a digit that does not match the winning number.
b. beginning with mmxx, make a complete list of the different possible arrangements of two matching digits and two digits that do not match, then find the probability for each entry in the list.
c. based on the results from part (b), what is the probability of getting exactly two matching digits when you select four digits for the win 4 lottery game?