The Medicare Plan D for prescription drugs for the elderly was announced in late 2005 and went into effect in 2006. The “base” plan is the following. Each person pays $384 per year and is then covered...

The Medicare Plan D for prescription drugs for the elderly was announced in late 2005 and went into effect in 2006. The “base” plan is the following. Each person pays $384 per year and is then covered as indicated in Table 10.6 (which comes directly from a Medicare informational Web site). In words, you pay the first $250, the plan pays 75% of the next $2000, you pay all of the next $2850, the so-called “coverage gap,” and the plan pays 95% of everything over $5100. (There are actually many such plans, all offered by private companies. The government stipulates that each such plan must be “at least as good as” the base plan described here.)

Suppose you believe that your drug expenses next year will be $2000, $3500, $5000, or $6500 with probabilities 0.2, 0.4, 0.3, and 0.1, respectively. If you join the base plan, what are your expected out-of-pocket expenses for the year?

Objective To illustrate the flaw of averages.