4. A manufacturing plant produces electronic circuit boards that need to pass two quality checks - a mechanical inspection and an electrical test. Historical data shows that \(15 \%\) of boards fail the mechanical inspection. Of those that pass the mechanical inspection, \(8 \%\) fail the electrical test. Of those that fail the mechanical inspection, \(60 \%\) fail the electrical test.

1. If a board is randomly selected from production, what is the probability that it passes both inspections?
2. If a board is selected at random and is found to have passed the electrical test, what is the probability that it also passed the mechanical inspection?
3. The company continues to test boards from a large batch until finding one that passes both inspections. Each board is tested independently of all others. What is the probability that they need to test exactly 3 boards to find one that passes both inspections?
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