A railway company randomly assigns both a carriage and a seat inthat carriage to customers on regional train services. The trainthat operates one regional route has two passenger carriages:

• Carriage A, which contains theon-board cafe, has 24 forwardfacing seats and 16 rear facing seats.

• Carriage B has 30 forward facing seats, and 30 rear facingseats.

  Since the route never carries more than 60 passengers (i.e., thecapacity of Carriage B), seats are assigned by first randomlyselecting a carriage, and then randomly selecting a seat withinthat carriage. To ensure seats around the cafe remain free,Carriage A is selected with a 25% probability.

  A passenger is pleased to find out they received a forwardfacing seat. What is the probability that the seat is in CarriageA?