Problem 4.(17pts) We have a random sample ofn-43 males agod 11 arthroscopic surg

Question

Problem 4.(17pts) We have a random sample ofn-43 males agod 11 arthroscopic surgery. They are classified according for injury type (twisted knee, direct t0 30 years with knee operations via and for surgical result (excellent, good, or fair-to-poor). Excellent Good Fair to poor Totals Twisted knee 21 Direct blow 3 Totals 36 2 24 13 43 a)3pts)Find the probability that a randomly selected male's injury type is Twisted knee and surgical result is Excellent bX4pts)Find the probability that a randomly selected male's injury type is Twisted knee. cX4pts) Find the probability that a randomly selected male's surgical result is Excellent given the injury type is Twisted knee. dX2pts) Are the events injury type and surgical result independent? (4pts) Why? Prove your answer using probability knowledge

Explanation / Answer

Solution:

total number of persons = 43

( a )

probability that the selected male's injury type is twisted knee and surgical result is excellent = 21/ 43 = 0.4883

( b )

probability that selected male's injury type is twisted knee = 36/43 = 0.8372

( c )

probability that selected male's surgical result is excellent given that ingury type is twisted knee = 21/36 = 0.5833

( d )

yes,the events injury type and surgical results are independant

Since, in the given table these two are the given seperately i.e., horizontally and vertically which forms the table

moreover, there is no such relationship between them to prove that they are dependant

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