This Is Why They Don't Do Joint Performance Reviews

Rajiv and Karthik are 2 traders at the Bank of Hyderabad, who are judged based on their daily Profit and Loss (P&L). Their boss was looking into their performance for the year, and wanted to know whether on a given day, they made money, lost money, or neither made nor lost any money (total of 3 distinct cases).

It was discovered that the probability that Rajiv neither made nor lost any money on a given day is 0.05. The probability that one of them neither made nor lost any money while the other did not make any money is 0.11. The probability that one of them neither made nor lost any money while the other did not lose any money is 0.23.

To 3 decimal places, what is the probability that Karthik neither made nor lost any money on a given day?

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