The document contains worked solutions to probability and math word problems. It includes: 1) A probability problem about the faces on a dice with non-standard numbering and calculating the chances of rolling each number. 2) A word problem about pulling socks from a drawer with different colored socks to be certain of getting a matching pair of blue socks. 3) A math word problem about students' test scores where the information given is used to set up and solve equations to find each individual score. 4) A final word problem about making a dye solution using water and dye in a specific ratio and calculating the amounts of each to use.

1. Exercise 15A – WORKED SOLUTIONS
Question 3
A wrongly numbered die (with faces 2, 3, 4, 5, 6, 6) is
thrown once. What is the probability that the face on top will be:
a) 2?
b) 3, 4 or 5?
c) 6?
P(N) =
# of likely outcomes
# of all possible outcomes
a)
1
6
b)
1
6
+
1
6
+
1
6
=
3
6
=
1
2
c)
2
6
=
1
3
Question 7
You have 10 blue socks, 4 black socks and 2 white socks in your drawer. Getting
dressed in the dark, you reach into the drawer. How many socks should you pull out to be
certain that you have a pair of blue socks?
This one is straight forward
Answer:
You’d need to get at least 6 as the first six could potentially black and white,
but then, you still need a pair of blue ones. Therefore, you’d need to take out
at least 10 individual socks to be guaranteed that you get a pair of blue socks
in the dark.

2. Exercise 15A – WORKED SOLUTIONS
Question 4
On a Science test, Brendan scored twice as many marks
as Damien but fifteen marks fewer than Maggie. The
total of the three scores is 205 marks. How much did each
student score on their Science test?
b = 2d
b = m-15
You don't have to write the above, but once you have this
worded as below, you can solve the question.
m = b +15
d =
1
2
b
b + m + d = 205
Replace m and d with what they equal.
1
b + b +15+ b = 205
2
2
1
2
b =190
b = 76
Once you know Brendan, you can now easilly work out the other
2 scores.
Damien = 1/2 b = 38
Maggie = 15+76 = 91
Question 10
In your science class you are asked to make up a 13.5-litre dye solution by using water
and dye in the ratio of 5 : 4. How many litres of each should you use?
5:4 = 13.5litres
1/9 x 13.5 = 1.5 litres per part.
Water = 5 parts = 5 x 1.5 = 7.5 litres
Dye = 4 parts = 4 x 1.5 = 6 litres

3. Exercise 15A – WORKED SOLUTIONS