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An insurance company hires its new staff from three agencies, A, B and C, in the...

An insurance company hires its new staff from three agencies, A, B and C, in the ratio 6:1:3. Its staff records show that 12% of recruits from Agency A, 15% of recruits from Agency B and 20% of recruits from Agency C have been judged “unsatisfactory” at the end of their first year. (a) What is the probability that a randomly selected recruit is judged “unsatisfactory”? (b) The company has just assessed a random sample of 15 recruits from a particular agency at the end of their first year and found 5 to be unsatisfactory. What is the probability that these 5 recruits were hired from Agency C?

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