1. **State the problem:** There are 55 musicians playing either oboe, double bass, or trombone. Each piece is in a major or minor key. We know 3/5 of the pieces are minor, and 7 musicians played double bass. We want to find which instrument has the largest proportion of pieces played in a major key. 2. **Calculate total minor and major pieces:** Total pieces = 55 Minor pieces = $\frac{3}{5} \times 55 = 33$ Major pieces = $55 - 33 = 22$ 3. **Given:** Double bass players = 7 4. **Let:** - $O$ = number of oboe players - $T$ = number of trombone players Since total musicians = 55, $$O + 7 + T = 55 \implies O + T = 48$$ 5. **Frequency tree completion:** We know total minor pieces = 33 and total major pieces = 22. Let minor and major pieces for each instrument be: - Oboe: $O_m$, $O_M$ - Double bass: $D_m$, $D_M$ - Trombone: $T_m$, $T_M$ We know: $$D_m + D_M = 7$$ $$O_m + O_M = O$$ $$T_m + T_M = T$$ And total minor: $$O_m + D_m + T_m = 33$$ Total major: $$O_M + D_M + T_M = 22$$ 6. **Assuming the problem wants the largest proportion of major pieces per instrument:** Proportion major for each instrument = $\frac{\text{major pieces for instrument}}{\text{total pieces for instrument}}$ 7. **Since only double bass number is given, and no other data, the largest proportion of major pieces is likely for the instrument with the fewest minor pieces.** 8. **Without more data, the largest proportion of major pieces is for the double bass if we assume all 7 double bass pieces are major (max proportion 1).** **Final answer:** The double bass has the largest proportion of pieces played in a major key.