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Faculty positions in a school district are classified as either teacher or admin

ID: 3074688 • Letter: F

Question

Faculty positions in a school district are classified as either teacher or administrator based on primary duties and responsibilities. The table below shows information on the number of national board-certified and not board-certified teachers and administrators.

Determine the probability, (board-certified or teacher), that a randomly chosen faculty member is either board-certified or a teacher. Please enter your answer as a decimal, precise to at least four decimal places.

(board-certified or teacher) =

Board-certified Not board-certified Administrator 10 6 Teacher 5 18

Explanation / Answer

Lets find column total and row total for given contingency table :

Addition rule for two event probability :

If A and B are two dependent event , then P( A or B)= P(A) + P( B )- P( A and B )

(board-certified or teacher) = P( Board-certified ) + P( Teacher) - P(board-certified and teacher)

Probability = number of favorable outcomes / total number of outcomes.

a) P( Board -certified) = Total number of board critified / Grand total .

   

P( Board -certified) = Total number of board critified / Grand total . = 15 / 39

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b ) P(Teacher ) Total number of teacher / Grand total

P(Teacher ) Total number of teacher / Grand total = 23 / 39

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c ) (board-certified and teacher) = number of board -certified and teacher / grand total.

(board-certified and teacher) = number of board -certified and teacher / grand total.

                                            = 5 / 39

Final answer :

(board-certified or teacher) = P( Board-certified ) + P( Teacher) - P(board-certified and teacher)

                                           =15/39 + 23/39 - 5 /39

                                          = 33/39 ==>>0.8462

Board-certified Not board-certified Total Administrator 10 6 16 Teacher 5 18 23 Total 15 24 39