Ink Inc., a publishing firm, offers its 899 employees a cafeteria approach to benefits, in which employees can enroll in the benefit plan of their choice. Seven hundred thirteen employees have health insurance, 523 have dental insurance, and 489 have both health and dental insurance. (a) What is the probability p that one of the employees has either health or dental insurance? (b) What is the probability p that one of the employees has health insurance but not dental insurance?
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(a) let 'has health insurance' be Set A and 'has dental insurance' be Set B. --start with the 'intersection'; A?B = 489 --then consider; has health insurance but not dental; ==> A union B compliment A?B´ = 713 - 489 = 224 --also 'has dental insurance but not health ==> A compliment union B A´?B = 523 - 489 = 34 --lastly: A?B = (A) + (B) - (A?B) = 713 + 523 - 489 = 747 P(has health insurance or dental) = 747/899 ? 0.8309 (b) P( has health insurance but not dental insurance) = 224/899 ? 0.2491
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