There is a 4% probability that the plane used for a commercial flight has technical problems, and this causes a delay in the flight. If there are no technical problems with the plane, then there is still a 33% probability that the flight is delayed due to all other reasons. What is the probability that the flight is delayed?

The solutions manual says 0.3568 but I can’t seem to get that answer. Could some one please explain how to do this problem? Thanks.

96 % of flights do not have a technical problem but then have a 33% chance of being delayed.
Multiply 96% times 33% is 31.68% of all flights.
Add the 4% of flights that do have a technical problem and we get the 35.68% – or .3568 probability.