A sandwich shop delivers lunches by bicycle to nearby office buildings. Unfortunately, sometimes the delivery is made later than promised. A delay can occur either because food preparation took too long, or because the bicycle rider got lost. Last month the food preparation took too long or the rider got lost, $7\%$ of the time. During the same month, the food preparation took longer than expected $11$ times and the bicycle rider got lost $4$ times. There were $200$ deliveries made during the month. For a randomly selected delivery last month, find the probability that both the food preparation took too long and the rider got lost.