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

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 Teacher 17 13 19 12 Determine the probability, P(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 P(board-certified or teacher)

Explanation / Answer

P( board - certified) = 30 / 61

P( Teacher ) = 25 / 61

P( board certified AND teacher = 13 / 61

P( A OR B ) = P(A) + P(B) - P( A AND B)

Therefore,

P( board-cerified OR Teacher) = P( board certified) + P( teacher) - P(board-cerified AND Teacher)

= 30 / 61 + 25 / 61 - 13/ 61

= 42 / 61

= 0.68852459

= 0.6885 (Rounded to four decimal places)

Board-Certified Non Board-Certified Total    Administrator 17 19 36 Teacher 13 12 25 Total 30 31 61

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