Mr. Zhang has a (1/3) probability of encountering a traffic jam when he goes to work every morning. When there is no traffic jam, the probability of Mr. Zhang arriving at the unit on time is 0.9, and the probability of being late is 0.1. When there is a traffic jam, Mr. Zhang is late for work. The probability is as high as 0.8, and the probability of arriving on time is only 0.2. May I ask: What is the probability that Mr. Zhang is late for work?
张先生每天早晨上班时有(1/3)的概率碰上堵车，在不堵车的时候，张先生按时到达单位的概率为0.9，迟到的概率为0.1；而堵车的时候，张先生上班迟到的概率高达0.8，按时到达的概率只有0.2．请问：张先生上班迟到的概率是多少？
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">0.8 * (1/3)</gadget>
<output>0.266667</output>

<gadget id="calculator">0.266667 + 0.1</gadget>
<output>0.366667</output>

<result>0.366667</result>