5) Suppose that from a group of 9 men, 1 will be randomly chosen for a dangerous

Question

5) Suppose that from a group of 9 men, 1 will be randomly chosen for a dangerous assignment, and suppose that the chosen man will be killed during the assignment with a probability of 1/6. If Mark is one of the 9 men, what is the probability that he will be chosen for the assignment and killed during the assignment? For this simple problem, I want you to carefully define pertinent events and show how the multiplication rule can be used to obtain the desired probability from the information that is given. (If this problem is chosen for grading, your grade will be largely determined by how well you follow the instructions. Obtaining the correct value for the probability without showing thorough justification, in the desired manner, will not earn much credit. (I hope that you develop the habit of carefully defining pertinent events for all problems of the types covered in Ch. 3 for which events are not defined in the statement of the problem.))

Explanation / Answer

Since one out of 9 men choosed the  dangerous assignment so the probability of choosing dangerous assignment is

P(dangerous assigment) = 1/9

And the chosen man will be killed during the assignment with a probability of 1/6 so

P(killed | dangerous assigment) = 1/6

By the mulitplication rule

P(killed and dangerous assigment) =P(killed | dangerous assigment) P(dangerous assigment) =(1/6)*(1/9)=54

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