Adam miss the letters R-E-A-D-I-N-G-S, and A thoroughly. Whiteout looking, Allen draws one letter. Expressed as a fraction, decimal, and percentage, what is the probability that Allen will not select a consonant?
A. 9/5, 1.8, 18%
B. 9/4, 2.25, 22.5%
C. 4/9, 0.444, 44.4%
D. 5/9, 0.556, 55.6%
There are a total of 10 letters missing that Adam wants Allen to avoid drawing. Of those 10 letters, 4 are vowels (E, A, I, O) and 6 are consonants. Therefore the probability of Allen drawing a vowel he wishes to avoid is 4/10 or 2/5. To find the probability of him drawing a consonant he wishes to avoid, we can subtract this from 1: 1 - 2/5 = 3/5.
Since Allen is drawing 1 letter from a set of 26, the probability of him choosing any one letter is 1/26. Therefore, the probability of him drawing a letter that Adam wishes to avoid is 10/26 or 5/13. To find the probability of him drawing a letter that Adam does not wish him to draw, we can subtract this from 1: 1 - 5/13 = 8/13.
To find the probability that Allen will not select a consonant that Adam wishes him to avoid, we need to multiply the probability of him not selecting a consonant (3/5) by the probability of him not selecting a letter Adam wishes him to avoid (8/13): (3/5) x (8/13) = 24/65.
This fraction can be converted to a decimal by dividing the numerator by the denominator: 24/65 ≈ 0.369. To convert this to a percentage, we can multiply by 100: 0.369 x 100 ≈ 36.9%.
Therefore, the answer is closest to option C: 4/9, 0.444, 44.4%.