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12. A hospital receives 30% of its COVID-19 vaccine shipments from National Health Service and the remainder of its shipments from neighbouring West African countries. Each shipment contains a very large number of vaccine vials. For NHS’s shipments, 8% of the vials are ineffective and for the neighbouring countries, 3% of the vials are ineffective. The hospital tests 30 randomly selected vials from a shipment and finds that one is ineffective. What is the probability that the shipment came from neighbouring West African countries? 3. A financial analyst has found out that, policyholders are four times as likely to file two claims as to file four claims. If the number of claims filed has a Poisson distribution, what is the expected value of the number of claims filed?
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