To find the probability that a randomly selected person talked less than 600 minutes given that they are a man, we can use the formula for conditional probability:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
Where:
- \( A \) is the event that a person talked less than 600 minutes.
- \( B \) is the event that the person is a man.
From the data given:
- The number of men surveyed is the sum of all the men, which is:
\[ 74 + 13 + 20 + 19 = 126 \]
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Therefore, the total number of men, \( P(B) \), equals 126.
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The number of men who talked less than 600 minutes, \( P(A \cap B) \), is 74 (given).
Now, substituting these values into the formula:
\[ P(A|B) = \frac{74}{126} \]
Calculating that:
\[ P(A|B) \approx \frac{74}{126} \approx 0.5889 \]
Thus, the probability that a randomly selected person talked less than 600 minutes given that they are a man is approximately
\[ 0.5889 \]
So, rounding to four decimal places, the answer is
\[ \boxed{0.5889} \]