Horace turns up at school either late or on time. He is then either shouted at or not. The probability that he turns up late is $0.4.$ If he turns up late, the probability that he is shouted at is $0.7$. If he turns up on time, the probability that he is still shouted at for no particular reason is $0.2$.

You hear Horace being shouted at. What is the probability that he was late?

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