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.

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

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) =

Answer 1

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

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

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 .

   

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

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

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

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

?(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