The names, or notes, of all the white keys on a piano are written on pieces of paper and placed in a cup. There are 7 sets of the notes D, E, F, and G and 8 sets of the notes A, B,and C. If a person draws one note out of the cup without looking, what are his or her chances of getting a C
total notes: 7*4 + 8*3 = 52
total C's: 8
so, . . .
15%
To calculate the chances of getting a C, we need to determine the total number of white keys on a piano and the number of C notes in the given scenario.
1. Start by counting the total number of white keys on a piano. There are a total of 12 unique notes in a full octave, including both black and white keys. However, we are only interested in the white keys, so there are 7 white keys in an octave.
2. The scenario states that there are 8 sets of the notes A, B, and C. Since each set likely contains one note of each kind, there are 8 C notes in the cup.
3. Next, calculate the total number of notes in the cup. There are 7 sets of D, E, F, and G notes, and each set contains one of each note. Thus, there are 7 × 4 = 28 D, E, F, and G notes. Additionally, there are 8 sets of A, B, and C notes, totaling 8 × 3 = 24 A and B notes. Finally, there are 8 C notes.
4. Now, add up the number of C notes: 8.
5. Finally, divide the number of C notes by the total number of notes in the cup to find the chances of getting a C: 8 / (28 + 24 + 8) = 8 / 60 ≈ 0.1333.
Therefore, the chances of drawing a C note from the cup without looking are approximately 0.1333 or 13.33%.