(1) Derive the probability density function of Y

II.1. The recruitment channels for a company are as follows: based on past experience, 50% of applicants learned of the openings through job banks, 10% through social media ads, 30% through employee referrals, and 10% through campus recruiting. The one-year turnover rates (the probability of an employee resigning within a year) are as follows: 10% for those from job banks, 20% for those from social media ads, 5% for those from employee referrals, and 30% for those from campus recruiting. If an employee is still with the company after one year, what is the probability that he (she) originally learned about the recruitment information through a job bank? (7%)

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(1) Derive the probability density function of \( Y \)

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