In: Statistics and Probability
Otto is considering flying his hot air balloon over a lake, yet he is concerned about his safety.
The hot air balloon has three independent burners, any one of which is sufficient to keep the balloon aloft. Otto knows that the probability that any individual burner will fail during this voyage is equal to .02.
Otto is only willing to go on this voyage if the probability that all three burners fail is less than .0000001.
Imagine that Otto asks you whether or not he should go on this voyage.
Would you advise Otto to go on this voyage? Justify your response with a calculation.