A bag contains tiles with the letters C-O-M-B-I-N-A-T-I-O-N-S. Lee chooses a tile without looking and doesn’t replace it. He chooses a second tile without looking. What is the probability that he will choose the letter O?
A. 1/132
B. 1/72
C. 1/66
D. 1/23
There are a total of 13 letters in the word COMBINATIONS. After Lee chooses a letter the first time, there will be one less letter in the bag. Therefore, there will be 12 letters in the bag for the second draw.
The probability of choosing O on the first draw is 2/13 (there are two O's in COMBINATIONS and a total of 13 letters).
If Lee did not choose an O on the first draw, there will be only one O left in the 12 letters in the bag for the second draw. Therefore, the probability of choosing O on the second draw after not choosing O on the first draw is 1/12.
The total probability of choosing O on either the first or second draw is the sum of the two probabilities:
2/13 + (11/13)(1/12) = 2/13 + 11/156 = 23/156
Therefore, the answer is D, 1/23.