(a) A number is selected at random from each of the sets {2, 3, 4} and {1, 3, 5}. What is the probability that the sum of the two numbers will be less than 7 but greater than 3?
(b)
In the diagram, ABCD is a circle. DAE, CBE, ABF and DCF are straight lines. If y + m = 90^\circ, find the value of x.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
+
1
3
5
2
3
5
7
3
4
6
8
4
5
7
9
Sample space = 9
Sum greater than 3 but less than 7 = {5, 4, 6, 5} = 4
P(sum greater than 3 but less than 7) = \(\frac{4}{9}\).
(b) Given that y + m = 90^\circ
< ABE = x^\circ (vertically opp. angles)
< BAD = (x + m)^\circ (exterior angles)
< DCB = (x + y)^\circ (exterior angles)
(x + m)^\circ + (x + y)^\circ = 180^\circ (opp. angles of a cyclic quadrilateral)
(2x + y + m)^\circ = 180^\circ
(2x + 90) = 180
2x = 180 - 90 = 90^\circ
x = 45^\circ
Source: Myschool Past Questions Archive (Record #54433)