حل السؤال 23، 4MA1/1HR يونيو 2020: المخططات الشجرية للأحداث المترابطة

1. 1Total beads = 3 + 4 + x = 7 + x
2. 2P(two blue) = (3/(7+x)) × (2/(6+x))
3. 3P(two white) = (4/(7+x)) × (3/(6+x))
4. 4P(two orange) = (x/(7+x)) × ((x−1)/(6+x))
5. 5Sum of probabilities = 3/8
6. 6(3×2 + 4×3 + x(x−1)) / ((7+x)(6+x)) = 3/8
7. 7(6 + 12 + x² − x) / (x² + 13x + 42) = 3/8
8. 8(x² − x + 18) / (x² + 13x + 42) = 3/8
9. 98(x² − x + 18) = 3(x² + 13x + 42)
10. 108x² − 8x + 144 = 3x² + 39x + 126
11. 115x² − 47x + 18 = 0
12. 12(5x − 2)(x − 9) = 0
13. 13x = 9 (since x must be a positive integer)
14. 14Total beads = 7 + 9 = 16

Answer16