A barrel contains 12 oranges, 8 grapefruit, and 5 apples for a total of 25 pieces of fruit. As a game, several friends took turns randomly extracting a single piece of fruit from the barrel blindfolded. If the extracted piece of fruit was not an apple, it was returned to the bin. This process was repeated until an apple was drawn. What is the probability that an apple will be extracted on the third extraction or later? Select the correct option: A) 5/25 B) 8/25 C) 12/25 D) 16/25 E) 4/5
Favorable case = an apple is picked in the third extraction or later.   Unfavorable case = an apple is picked in either the first or second extraction.   Probability = Favorable outcomes / Total out comes   Also probability = 1-(Unfavorable outcomes / Total out comes)   Unfavorable case 1: probability of apple picked in first extraction = 5/25   Unfavorable case 2: probability of apple picked in second extraction (i.e., 2nd extraction not an apple)= (20/25)*(5/25) =(4/5)*(1/5)= 4/25   Total Unfavorable Probability = (5/25)+(4/25) = 9/25   i.e., Favorable Probability = 1 - (9/25) = 16/25   Answer Option: 16/25
<result>D</result>
A barrel contains 12 oranges, 8 grapefruit, and 5 apples for a total of 25 pieces of fruit. As a game, several friends took turns randomly extracting a single piece of fruit from the barrel blindfolded. If the extracted piece of fruit was not an apple, it was returned to the bin. This process was repeated until an apple was drawn. What is the probability that an apple will be extracted on the third extraction or later?