2013 DSE Maths Paper 1 Q10

10
(a) :
Required Median = 31
Required Mode = 23

(b)(i):

(6x10+b) - (2x10+a) = 47
40+a+b = 47
a+b = 7
∵ 0 ≦ a ≦ 5
7≦b ≦ 9
∴The solutions are a=0,b=7 / a=1,b=8 / a=2,b=9

(b)(ii):
Required probability =
3+3+2+2+2+2+2x3+4x3÷13x20 = 8/65