Suppose that in our league, half of mlb batters have a “true talent” on-base percentage (“obp” or the probability that a batter gets on base in a plate appearance) of .310 and the other half have a true-talent on-base percentage of .350. in scanning the season-to-date batting statistics, you see that billy bases has gotten on base 35 times in 100 plate appearances. without any additional information about billy’s performance so far this season, what is the probability that his “true-talent” obp matches his current obp of .350?

The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. complete parts (a) and (b) below. business degrees nonbusiness degrees total male 189131 634650 823781 female 169539 885329 1054868 total 358670 1519979 1878649 (a) find the probability that a randomly selected student is male, given that the student received a business degree. the probability that a randomly selected student is male, given that the student received a business degree, is nothing. (round to three decimal places as needed.) (b) find the probability that a randomly selected student received a business degree, given that the student is female. the probability that a randomly selected student received a business degree, given that the student is female, is nothing. (round to three decimal places as needed.)