A survey asked business travelers if they worked harder on a business trip. Fifty percent of the respondents were younger than 45 years and the other 50% where 45 years or older. Sixty-four percent of the younger respondents indicated they did work harder on business trips while 30% of the older respondents indicated they worked harder on business trips. Given that the respondent indicated he/she worked harder on business trips, use Bayes' Theorem to determine the probability that the person is younger than 45 years old. Show all supporting work.

Note: this problem does not require Excel.