Question

In the November 27, 1994, issue of Parade magazine, the "Ask Marilyn" section contained this question: "Suppose a person was having two surgeries performed at the same time. If chances of success for surgery A are 85%, and the chances of success for surgery B are 90%, what are the chances that both would fail?" What do you think of Marilyn's solution: (0.15) (0.10) = .015?

a. Her solution is mathematically correct but not explained very well.
b. Her solution is both mathematically correct and intuitively obvious.
c. Her use of complementary events is incorrect.
d. Her use of the general addition formula is incorrect.
f. She assumed independence of events, which is most likely wrong.

Answer 1

Marilyn correctly calculated the probability of both surgeries failing by multiplying the individual probabilities of failure for each surgery, assuming the surgeries are independent. The probability is 1.5% or 0.015.

Step-by-step explanation:

The question you've asked is related to probability, specifically the calculation of the likelihood of two independent events both failing. The 'Ask Marilyn' segment in Parade magazine on November 27, 1994, answered this question with Marilyn stating that the probability of both surgeries failing is calculated by multiplying the probability of each surgery failing.

If surgery A has an 85% chance of success, it means it has a 15% chance of failure (100% - 85%), represented as 0.15. For surgery B with a 90% chance of success, the failure chance is 10% (100% - 90%), represented as 0.10. When multiplying these probabilities (0.15 x 0.10), we get 0.015 or 1.5%, which is the probability that both surgeries will fail.

This calculation assumes that the events, the two surgeries, are independent, meaning the outcome of one does not affect the outcome of the other.

In real-life medical scenarios, surgeries may not be perfectly independent; however, in terms of probability theory, and without additional information suggesting otherwise, treating the events as independent is a common and acceptable assumption.

The letter selection provided does not offer an exact match to the explanation given, but the closest one would be option a. Her solution is mathematically correct but not explained very well, as Marilyn did not provide much elaboration on why these probabilities are multiplied or the assumption of independence.