Alice is considering purchasing critical illness insurance for herself. The policy has an annual cost of $5000. And if Alice has been diagnosed with any critical illness within the year of insurance, she would be compensated up to $150,000 (the maximum claim amount). If there is no insurance coverage, an early stage of critical illness (e.g., cancer) would cost about $10,000; an advanced stage of critical illness would cost about $200,000.

Based on Alex’s family profile, the estimated probabilities that an early stage of critical illness and an advanced stage of critical illness would occur are around 3% and 1% respectively.

(a) Using the expected value approach, what decision would Alice make?

(b) If Alice chooses to buy the insurance anyway, what would be the most realistic reason for this decision?