Question 61

The probability that the patient has insurance coverage from either Medicare or Medicaid is 55%.

To find the probability of a patient having insurance coverage from either Medicare or Medicaid, we use the formula for the union of two events: P(Medicare ∪ Medicaid) = P(Medicare) + P(Medicaid) - P(Medicare ∩ Medicaid). Substituting the values, we get 0.45 + 0.25 - 0.15, which equals 0.55, or 55%.

A) 85%

This option is incorrect because it suggests that the combined probability of having either Medicare or Medicaid coverage is higher than the individual probabilities. The calculations show that the correct total is significantly lower.

B) 55%

This option is correct as it accurately reflects the calculated probability based on the given values. Utilizing the formula for the union of two probabilities, the result confirms that 55% is the appropriate answer.

C) 40%

This option is incorrect as it underestimates the combined probability. The calculation of 55% clearly indicates that the total is higher than 40%, making this choice unviable.

D) 70%

This option is incorrect because it overestimates the combined probability of insurance coverage from Medicare or Medicaid. The correct calculation yields a probability of 55%, making 70% an inaccurate representation.

Conclusion

The correct answer of 55% is derived from applying the union probability formula, which accurately accounts for the overlap between Medicare and Medicaid coverage. All other options fail to represent the correct total, either overestimating or underestimating the probabilities involved. Thus, 55% is definitively the right answer for the probability of having insurance coverage from either source.