In Orange County, 51% of the adults are males. One adult is randomly selected for a survey involving credit card usage. It is later learned that the selected survey subject was smoking a cigar. Also, 9.5% of males smoke cigars, whereas 1.7% of females smoke cigars (based on data from the Substance Abuse and Mental Health Services Administration). Use this additional information to find the probability that the selected subject is a male.
A person uses his car 30% of the time, walks 30% of the time and rides the bus 40% of the time as he goes to work. He is late 10% of the time when he walks; he is late 3% of the time when he drives; and he is late 7% of the time he takes the bus.
In a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
On a game show, a contestant can select one of four boxes. The red box contains one $\$100$ bill and nine $\$1$ bills. A green box contains two $\$100$ bills and eight $\$1$ bills. A blue box contains three $\$100$ bills and seven $\$1$ bills. A yellow box contains five $\$100$ bills and five $\$1$ bills. The contestant selects a box at random and selects a bill from the box at random. If a $\$100$ bill is selected, find the probability that it came from the yellow box.